title: Ram Mohan

abstract: Ram Mohan was an Indian animator, title designer and design educator, who was also known as father of Indian Animation and was a veteran in the Indian animation industry, who started his career at the Cartoon Films Unit, Films Division of India, Government of India in 1956. He was chairman and chief creative officer at Graphiti Multimedia, a Mumbai-based animation company which was established in 1995, and later he also established the Graphiti School of Animation in 2006. He had won the National Film Award for Best Non-Feature Animation Film twice, You Said It (1972) and Fire Games (1983). He was awarded a lifetime achievement award at the 2006 Mumbai International Film Festival and was awarded the Padma Shri the fourth-highest civilian award given by Government of India in 2014.

text:
# Ram Mohan

**Ram Mohan** (26 August 1931 – 11 October 2019) was an Indian animator, title designer and design educator, who was also known as father of Indian Animation and was a veteran in the Indian animation industry, who started his career at the Cartoon Films Unit, Films Division of India, Government of India in 1956. He was chairman and chief creative officer at Graphiti Multimedia, a Mumbai-based animation company which was established in 1995, and later he also established the Graphiti School of Animation in 2006.

He had won the National Film Award for Best Non-Feature Animation Film twice, *You Said It* (1972) and *Fire Games* (1983). He was awarded a lifetime achievement award at the 2006 Mumbai International Film Festival and was awarded the Padma Shri the fourth-highest civilian award given by Government of India in 2014.

## Early life and education

Graduated in Chemistry from the University of Madras and later moved to Mumbai for his post-graduate studies but gave it up to join the Cartoon Films Unit, Films Division, Government of India in 1956. He received training in animation techniques from Clair Weeks of Walt Disney Studios, under the US Technical Aid program. Weeks was at the time serving a two-year stint as the head of the Cartoon Films Unit. Another important person to join at the same time was Bhimsain Khurana, who also became a notable animator (*Ek Anek Aur Ekta*).

## Career

Mohan worked as an animator with the Films division till the late 1960s, and thereafter founded Ram Mohan Biographics, in 1972. It ultimately merged with UTV Toons, a division of United Studios Limited (USL) in 1998.

Mohan started out by doing character design and story boards for *This Our India*, an animated film adapted from a book by Minoo Masani. He scripted, designed and animated many of Cartoon Film unit's productions from 1960 to 1967, including 'Homo Saps' which won the National Award for Best Experimental Film, 1967, and 'Chaos' which won an Award at the Leipzig Festival of short Films in 1968. He participated in the 1967 world retrospective of Animation Cinema in Montreal.

In 1968 he left Films Division and joined Prasad Productions as chief of their animation division. In 1972, he established his own production company, Ram Mohan Biographics, which worked on commercials, and the animated feature *Ramayana: The Legend of Prince Rama* (1992), which he co-directed in collaboration with Yugo Sako from Japan.

Ram Mohan's film credits include several animation sequences for mainstream filmmakers – an animated song for B.R. Chopra's *Pati Patni Aur Woh* (1978), a title sequence for Satyajit Ray's *Shatranj Ke Khilari*, a sequence for Mrinal Sen's Hindi film, *Bhuvan Shome*, and for films such as *Biwi-O-Biwi*, *Do Aur Do Paanch* and *Kaamchor*.

Ram Mohan was also responsible for the spread of animation in India. Many of the leading animation professionals active today in India started their careers in his studio.

## Death

Ram Mohan died on 11 October 2019 in Mumbai at the age of 88.

## Filmography

| Film | Year | Role | Notes |
| --- | --- | --- | --- |
| *Certificate of Security* | 1962 | Animator |  |
| *Building A Nest* | 1962 | Animator |  |
| *Healthy and Happy* | 1962 | Assistant animator |  |
| *Mansube Machlidar* | 1963 | Animator |  |
| *Exploration of Upper Air* | 1964 | Animator |  |
| *A Fable Retold* | 1965 | Animator |  |
| *That Touch of Gold* | 1966 | Animator |  |
| *Homo Saps* | 1966 | Animator |  |
| *That Bright Touch* | 1966 | Animator |  |
| *Dreams of Mauji Ram* | 1966 | Animator |  |
| *Shadow and Substance* | 1967 | Animator and script writer |  |
| *Sandesh* | 1967 | Organization (*Aayojan*) |  |
| *Paint Paint Paint* | 1968 | Animator |  |
| *Shadow Across The East* | 1968 | Director |  |
| *Baap Re Baap* | 1968 | Director | Animated short film
National Award for the Best Film on family planning |
| *Haseena Maan Jayegi* | 1968 | Animation Director | Title sequence |
| *Bhuvan Shome* | 1969 | Animation Artist |  |
| *Chaos* | 1969 | Director | Animated short film |
| *Jitana Chhotta Ho Parivar* | 1971 | Animator |  |
| *The Cheats* | 1971 | Commentry Words |  |
| *Chain Reaction* | 1971 | Commentry Words |  |
| *The Ultimate Ruler* | 1972 | Script Writer |  |
| *You Said It* | 1972 | Director, Script Writer and designer | Animated short film
National Film Award for Best Non-Feature Animation Film |
| *Bholu Ki Bakari* | 1976 | Script Writer |  |
| *An Evergreen Story* | 1976 | Guidance |  |
| *Shatranj Ke Khilari* | 1977 | Animation Director |  |
| *Tobacco Habits and Oral Cancer* | 1978 | Animator |  |
| *Pati Patni Aur Woh* | 1978 | Animation Director | Song "Na Aaj Tha Na Kal Tha" |
| *Precious Water (Anmol Pani)* | 1980 | Script Writer |  |
| *In The Service of Mankind* | 1980 | Animator |  |
| *The Human Body* | 1980 | Director |  |
| *Do Aur Do Paanch* | 1980 | Animation Director | Title sequence |
| *Khubsoorat* | 1980 | Animation | Song "Qayda Qayda" |
| *Insaf Ka Tarazu* | 1980 | Title Design |  |
| *Biwi-O-Biwi* | 1981 | Animation Director | Title sequence |
| *Swar Sangam* | 1981 | Animation Director |  |
| *Kaamchor* | 1982 | Animation Director |  |
| *Angoor* | 1982 | Animation by Ram Mohan Biographics |  |
| *The Continuous Line* | 1983 | Graphics by Ram Mohan Biographics |  |
| *Fire Games* | 1983 | Director and designer | Animated short film
National Film Award for Best Non-Feature Animation Film |
| *The Four Steps* | 1984 | Commentry Words |  |
| *Taru* | 1989 | Director and designer |  |
| *Ramayana: The Legend of Prince Rama* | 1992 | Director(with Yugo Sako) | Animated feature-length film Indo-Japanese co-production |
| *Meena* | 1993–2001 | Director(16 episodes from 1993 to 2001)
Storyboard artist(3 episodes from 1993 to 1995) | Animated children's television show created by UNICEF |
| *O' Faby* | 1993 | Animation Director | Malayalam Film |
| *The Pea Plant Legacy (Three Part Series)* | 2015 | Script writer, Director and executive Producer |  |

## Awards

* 1969– National Award for the Best Film on family planning, "Baap Re Baap".
* 1972– National Film Award for Best Non-Feature Animation Film: *You Said It*
* 1974– He was commissioned to script, design and direct a series of educational films on population and environment, "Down to Earth" for the International Planned Parenthood Federation and the Family Planning Association of India.
* 1983 – National Award for the Best Animation Film: *Fire Games*
* 1996– Communication Arts Guild Hall of Frame award for Life Time achievement. Series director:"Meena" for UNICEF, a series of 13 episodes dealing with issues concerning the girl child in south Asia.
* 2001– Advertising Club Award 'ABBY' for Life Time Achievement.
* 2003– I.D.P.A. 'Ezra Mir' award for Life-Time Achievement. Broadcast India
* 2014 – Padma Shri, India's 4th highest civilian award by Govt. of India.

## Bibliography

## InfoBox

| Ram Mohan | |
| --- | --- |
|  | |
| Born | (1931-08-26)26 August 1931 |
| Died | 11 October 2019(2019-10-11) (aged 88)
Mumbai, Maharashtra |
| Nationality | Indian |
| Occupation(s) | Animator
Founder, Graphiti Multimedia (1995) |
| Known for | You Said It (1972)
Fire Games (1983)
*Ramayana: The Legend of Prince Rama* (1992)
*Meena* (1993–2001) |
| Awards | Padma Shri (2014) |


title: Caecum subannulatum

abstract: Caecum subannulatum is a species of minute sea snail, a marine gastropod mollusk or micromollusk in the family Caecidae.

text:
# Caecum subannulatum

***Caecum subannulatum*** is a species of minute sea snail, a marine gastropod mollusk or micromollusk in the family Caecidae.

## Description

## Distribution

## InfoBox

| *Caecum subannulatum* | |
| --- | --- |
|  | |
| Shell of *Caecum subannulatum* | |
|
| Scientific classification | |
| Domain: | Eukaryota |
| Kingdom: | Animalia |
| Phylum: | Mollusca |
| Class: | Gastropoda |
| Subclass: | Caenogastropoda |
| Order: | Littorinimorpha |
| Family: | Caecidae |
| Genus: | *Caecum* |
| Species: | ***C. subannulatum*** |
| Binomial name | |
| ***Caecum subannulatum***<br>de Folin, 1870 | |
|


title: Epeli Nailatikau

abstract: Brigadier-General Ratu Epeli Nailatikau, is a Fijian chief who was President of Fiji from 2009 to 2015. He has had a long career in the Military, diplomatic service, and government. From 2001 to 2006 he served as Speaker of the House of Representatives – the lower and more powerful chamber of the Fijian Parliament. He was also the chairman of the Parliamentary Appropriations Committee and of the House Committee. On 8 January 2007, he was appointed the interim Minister for Foreign Affairs and External Trade; he was moved to the post of interim Minister for Provincial Development and Multi-Ethnic Affairs in September 2008. In October 2008, he became Indigenous Affairs Minister "and effectively Great Council of Chiefs chairman". On 17 April 2009, he was appointed Vice-President by the military government. On 30 July 2009, he became acting president after the retirement of President Josefa Iloilo. On 5 November 2009, he was sworn in as President of Fiji. George Konrote was elected to succeed him in October 2015. On 11 February 2019, he became the newly appointed Speaker of the Fijian Parliament, winning 30 votes against 21 to Opposition nominee and Suva lawyer, Tanya Waqanika.

text:
# Epeli Nailatikau

Brigadier-General ***Ratu*** **Epeli Nailatikau**, CF, LVO, OBE, MSD, KStJ (born 5 July 1941) (often referred to as *Na Turaga Mai Naisogolaca*) is a Fijian chief who was President of Fiji from 2009 to 2015. He has had a long career in the Military, diplomatic service, and government. From 2001 to 2006 he served as Speaker of the House of Representatives – the lower and more powerful chamber of the Fijian Parliament. He was also the chairman of the Parliamentary Appropriations Committee and of the House Committee. On 8 January 2007, he was appointed the interim Minister for Foreign Affairs and External Trade; he was moved to the post of interim Minister for Provincial Development and Multi-Ethnic Affairs in September 2008. In October 2008, he became Indigenous Affairs Minister "and effectively Great Council of Chiefs chairman". On 17 April 2009, he was appointed Vice-President by the military government.

On 30 July 2009, he became acting president after the retirement of President Josefa Iloilo. On 5 November 2009, he was sworn in as President of Fiji. George Konrote was elected to succeed him in October 2015.

On 11 February 2019, he became the newly appointed Speaker of the Fijian Parliament, winning 30 votes against 21 to Opposition nominee and Suva lawyer, Tanya Waqanika.

## Education and military career

Born to a family of politically powerful chieftains, Nailatikau's career spanned 20 years in the military and 17 years in the diplomatic service. Following his education at Bau District School, Draiba Fijian School, Levuka Public School and Queen Victoria School, Nailatikau trained as a soldier in New Zealand. In 1966, he served on secondment in the 1st Battalion, Royal New Zealand Infantry Regiment and was posted to Sarawak, Malaysia, during Indonesia's "Konfrontasi" against Malaysia. He proved to be a popular and highly respected officer. When he returned to the Fiji Infantry Regiment, he rose steadily through the ranks. By 1987, he held the rank of Brigadier-General, and was the Commander of the Royal Fiji Military Forces. While visiting Australia, he was deposed from this position, however, when the third-ranked officer, Lieutenant-Colonel Sitiveni Rabuka staged the first of two coups and seized power.

## Diplomatic career

Nailatikau retired from the Army and decided to pursue a new career in the diplomatic service. After completing the Foreign Service Course at Oxford University in the United Kingdom, he was appointed High Commissioner to the United Kingdom and accredited as Fiji's ambassador to Denmark, Egypt, Germany, Israel and the Holy See. He was later appointed Fiji's roving ambassador and high commissioner to the member states of the South Pacific Forum, before taking up a post as Permanent Secretary for Foreign Affairs and External Trade in 1999.

## Political career

In the aftermath of the failure of the Fiji coup of 2000, a coup which Nailatikau strongly opposed, he was nominated for the position of Prime Minister, to help rebuild Fiji's shattered institutions. He withdrew his nomination, however, in favour of Laisenia Qarase, who was considered more of a consensus candidate, but became Deputy Prime Minister and Minister for Fijian Affairs in the interim Cabinet. He was appointed Deputy Prime Minister in August 2000. He was appointed again Deputy Prime Minister of Laisenia Qarase in 2001 and served until September 2001, when he was elected the Speaker. In 2001, after democracy had been restored in a general election, he defeated, by a vote of 41 to 29, Joeli Kalou for the position of Speaker of the House of Representatives, a position he held until after the 2006 elections.

Following the coup d'état of 5 December 2006, he was sworn in as Minister for Foreign Affairs and External Trade in the new interim government of Prime Minister Commodore Frank Bainimarama on 8 January 2007.

He was nominated to become the new vice-president by the Fiji president Ratu Josefa Iloilo on 10 April 2007, but was rejected by the GCC. On 17 April 2009, after Fiji experienced a constitutional crisis, Ratu Epeli was appointed vice president.

Nailatikau served as interim Minister of Foreign Affairs, International Co-operation and Civil Aviation under Prime Minister Frank Bainimarama, beginning in January 2007. On 23 September 2008, Bainimarama said that Nailatikau would be moved to the post of Minister for Provincial Development and Multi-Ethnic Affairs on 5 October 2008, while Bainimarama would take over his previous duties. According to Bainimarama, he "decided to give him this new responsibility given his extensive knowledge and hands-on experience on the workings of the Civil Service, Governments role in rural development and the sources of assistances available to facilitate such development", while also stating that Nailatikau had "excellent public relations appeal, which is very much needed in outreaching and inter-facing with rural people."

### Acting prime minister

On 25 September 2007, Epeli was appointed acting prime minister while interim Prime Minister, Frank Bainimarama, was away in New York for the week.

### Acting president

On 30 July 2009, he became acting president after the retirement of 88-year-old President Iloilo. The president was supposed to be appointed by the Great Council of Chiefs (effectively abolished by the military-backed regime) under the 1997 constitution that Iloilo had abrogated, but Bainimarama announced that a new president would be appointed by his cabinet at the regime's convenience. Nailatikau was formally appointed to the office on 5 November 2009.

## Anti-AIDS campaigner

On 14 June 2005, Nailatikau was appointed the UNAIDS special representative for the Pacific. According to the Joint United Nations Program on HIV/AIDS, he was chosen because his political position, his respect throughout the Pacific region, and his outspokenness on AIDS-related issues. He had previously served as a UNAIDS Pacific spokesman, and in October 2004 chaired the first conference of Pacific Parliamentarians on the Role of Pacific Parliamentarians in the fight against HIV/AIDS, in Suva.

Nailatikau's outspoken calls to tackle the AIDS crisis have attracted controversy. On 22 November 2005, he called on people to recognise the reality that promiscuity existed, and that safe sex needed to be promoted to combat the associated AIDS risk. It was unrealistic to deny promiscuity and just promote abstinence, he considered, adding that this was a matter of life and death. He also called on churches to face the reality that promiscuity existed among their own congregations, and to meet the problem "head on" and play a part in promoting the use of condoms.

He represented the Commonwealth Parliamentary Association (CPA) at the World AIDS Conference in Toronto in August 2006.

## Personal life

As a chief by birth through his paternal side via his maternal grandmother, who is the granddaughter of Ratu Seru Cakobau, Epeli Nailatikau has the title of *Ratu*. He is the second son of Ratu Edward Cakobau, who commanded the Fijian Battalion in World War II. He is also a great-great-grandson of Seru Epenisa Cakobau from his granddaughter Litia Cakobau, the first monarch to rule over a unified Fijian kingdom after conquering all the tribes of Fiji and uniting them under his leadership, and who ceded the Fiji Islands to the United Kingdom in 1874. In addition, he is a grandson of King George Tupou II of Tonga. His father is the product of issue between King George Tupou II and Litia Cakobau who was sent to Tonga as a trial bride to the King but this was later repudiated as they could not marry under the normal Tongan constitution.

In 1981, he married Adi Koila Mara, the second daughter of modern Fiji's former prime minister and president Ratu Sir Kamisese Mara. Adi Koila has also been a politician; like her husband, she was a Member of Parliament, Cabinet minister, and Senator. They have two children: a son, Kamisese Vuna (named after Adi Koila's father), and a daughter, Litia Cakobau.

## Honours

### National honours

### Foreign honours

## InfoBox

| Brigadier-General the Honourable *Ratu*Epeli NailatikauCF LVO OBE MSD KSTJ | |
| --- | --- |
|  | |
|  | |
| 2nd Speaker of the Parliament | |
| **In office**
11 February 2019  24 December 2022 | |
| Prime Minister | Frank Bainimarama |
| Preceded by | Jiko Luveni |
| Succeeded by | Naiqama Lalabalavu |
| President of Fiji | |
| **In office**
30 July 2009  12 November 2015
Acting: 30 July 2009 – 5 November 2009 | |
| Prime Minister | Frank Bainimarama |
| Preceded by | Josefa Iloilo |
| Succeeded by | George Konrote |
| Speaker of the House of Representatives of Fiji | |
| **In office**
2001–2006 | |
| Preceded by | Apenisa Kurisaqila |
| Succeeded by | Pita Nacuva |
| Vice-President of Fiji | |
| **In office**
17 April 2009  30 July 2009 | |
| President | Josefa Iloilo |
| Preceded by | Joni Madraiwiwi (2006) |
| Succeeded by | *Office Abolished* |
| Deputy Prime Minister of Fiji | |
| **In office**
August 2000  2001 | |
| Prime Minister | Laisenia Qarase |
| Succeeded by | Tupeni Baba |
| **In office**
2001  September 2001 | |
| Prime Minister | Laisenia Qarase |
| Preceded by | Tupeni Baba |
|  | |
| Personal details | |
| Born | (1941-07-05) 5 July 1941
Suva, Colony of Fiji |
| Political party | Independent |
| Spouse | Adi Koila Mara (m. 1981) |
| Children | 2 |
| Parent |  |
|  | |


title: Courtagnon

abstract: Courtagnon is a commune in the Marne department in north-eastern France.

text:
# Courtagnon

**Courtagnon** (French pronunciation: \[kuʁtaɲɔ̃\]) is a commune in the Marne department in north-eastern France.

## InfoBox

| Courtagnon | |
| --- | --- |
| Commune | |
| The town hall in Courtagnon | |
| Location of Courtagnon | |
| CourtagnonCourtagnon | |
| Coordinates: 49°08′43″N 3°56′49″E / 49.1453°N 3.9469°E / 49.1453; 3.9469 | |
| Country | France |
| Region | Grand Est |
| Department | Marne |
| Arrondissement | Reims |
| Canton | Fismes-Montagne de Reims |
| Intercommunality | CU Grand Reims |
| Government | |
| Mayor (20202026) | Valérie Cordebar |
| Area**1** | 3.95 km2 (1.53 sq mi) |
| Population (2021) | 72 |
| Density | 18/km2 (47/sq mi) |
| Time zone | UTC+01:00 (CET) |
| Summer (DST) | UTC+02:00 (CEST) |
| INSEE/Postal code | 51190 /51480 |
| Elevation | 180 m (590 ft) |
| **1** French Land Register data, which excludes lakes, ponds, glaciers \> 1 km2 (0.386 sq mi or 247 acres) and river estuaries. | |


title: Rune Lund

abstract: Rune Lund is a former Danish politician, who was a member of the Folketing for the Red–Green Alliance political party. He was elected at the 2015 Danish general election, and previously sat in parliament from 2005 to 2007.

text:
# Rune Lund

**Rune Lund** (born 30 October 1976 in Copenhagen) is a former Danish politician, who was a member of the Folketing for the Red–Green Alliance political party. He was elected at the 2015 Danish general election, and previously sat in parliament from 2005 to 2007.

## Political career

Lund was first elected into parliament at the 2005 election. He was not reelected in 2007, but received enough votes to become the Red-Green Alliance's primary substitute in the Fyn constituency. In the 2015 election he received 530, but the Red-Green Alliance received enough overall votes for several levelling seats, one of which went to Lund. He was reelected in 2019 Danish general election with 1,157 votes, which was enough for a direct seat in parliament. He stepped down from the Folketing in 2022 and moved to Kenya. He now works as the East Africa manager for Danish software company cBrain.

## InfoBox

| Rune Lund | |
| --- | --- |
|  | |
| Member of the Folketing | |
| **In office**
18 June 2015  2022 | |
| Constituency | Copenhagen |
| **In office**
8 February 2005  13 November 2007 | |
| Constituency | Fyn |
|  | |
| Personal details | |
| Born | (1976-10-30) 30 October 1976
Copenhagen, Denmark |
| Political party | Red–Green Alliance |
|  | |


title: San Simeon, California

abstract: San Simeon is an unincorporated community on the Pacific coast of San Luis Obispo County, California, United States. Its position along State Route 1 is about halfway between Los Angeles and San Francisco, each of those cities being roughly 230 miles (370 km) away. A key feature of the area is Hearst Castle, a hilltop mansion built for William Randolph Hearst in the early 20th century that is now a tourist attraction. The area is also home to a large northern elephant seal rookery, known as the Piedras Blancas rookery, located 7 miles (11 km) north of San Simeon on Highway 1.

text:
# San Simeon, California

**San Simeon** (Spanish: *San Simeón*, meaning "St. Simon") is an unincorporated community on the Pacific coast of San Luis Obispo County, California, United States. Its position along State Route 1 is about halfway between Los Angeles and San Francisco, each of those cities being roughly 230 miles (370 km) away. A key feature of the area is Hearst Castle, a hilltop mansion built for William Randolph Hearst in the early 20th century that is now a tourist attraction. The area is also home to a large northern elephant seal rookery, known as the Piedras Blancas rookery, located 7 miles (11 km) north of San Simeon on Highway 1.

## History

Humans first settled the local area at least 11,000 years ago. Prehistorically, the local area was inhabited by the Chumash people, including a large village south of San Simeon at Morro Creek.

In 1542 the coastal exploration of Juan Cabrillo discovered the bay and named it the Bay of Sardines.

The first European land exploration of Alta California, the Spanish Portolà expedition, traveled northwest along the coast in September 1769. On September 11–12, the party passed the future location of San Simeon. At Ragged Point, which is about 15 mi (24 km) past San Simeon, the party turned inland across the Santa Lucia Range.

San Simeon was founded as an *asistencia* ("sub-mission") to Mission San Miguel Arcángel, founded in 1797 and located to the east across the Santa Lucia Range. The Bay of San Simeon is mentioned in the records of San Miguel Mission for 1830. San Simeon was named for Rancho San Simeon, although the town-site is actually north of that rancho, on the former Rancho Piedra Blanca, a Mexican land grant given in 1840 to José de Jesús Pico. In 1865, Pico sold part of the rancho to George Hearst, the father of William Randolph Hearst.

The first Europeans to settle in the immediate area near the bay of San Simeon were Portuguese shore whalers under the command of Captain Joseph Clark (born Machado) from the Cape Verde Islands, around 1864. In 1869, Captain Clark built a wharf near the point for his whaling station. A small community grew near the 1869 wharf, but the waves near the wharf were too high, and the wharf was abandoned. In 1878, Hearst built a new wharf, and the small community moved near the new wharf. A general store (later Sebastian's Store) was built near the Clark wharf, and then relocated near the 1878 wharf. Shore whaling continued on the point until the mid-1890s. It ceased for a short time, started up again in 1897, and continued until about 1908 when it ceased for good.

In 1953, the Hearst Corporation donated the William Randolph Hearst Memorial Beach, including the Hearst Pier, to San Luis Obispo County. It is currently part of Hearst San Simeon State Park. The present-day San Simeon pier was built in 1957.

## Geology

The name *San Simeon* also refers to some geologic structures of the area, particularly elements of the coastal Jurassic-age landforms and ophiolite rock formations.

## Geography

According to the United States Census Bureau, the census-designated place covers an area of 0.8 square miles (2.1 km2), all of it land. The original townsite of San Simeon is at San Simeon Bay, and was the important 19th-century shipping point with the successive wharves that were built. San Simeon Acres, about 4 mi south of the original townsite at the mouth of Pico Creek, and so about halfway between old San Simeon and Cambria, was established in the 1950s. Most of the development at San Simeon Acres was in the 1960s to the 1980s. Many motels and cafes serve visitors to Hearst Castle.

### Climate

San Simeon and the Hearst Castle area has a warm-summer Mediterranean climate (Köppen *csb*) that is moderated by its relative proximity to the Pacific coastline. NOW Data has readings from the San Simeon weather station since December 1999.

| Climate data for San Simeon, California (Hearst Castle), 1999–2020 averages, extremes 1999–present | | | | | | | | | | | | | |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Month | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | Year |
| Record high °F (°C) | 84
(29) | 83
(28) | 85
(29) | 95
(35) | 94
(34) | 102
(39) | 101
(38) | 102
(39) | 109
(43) | 100
(38) | 89
(32) | 80
(27) | 109
(43) |
| Mean maximum °F (°C) | 74.6
(23.7) | 73.9
(23.3) | 76.8
(24.9) | 81.9
(27.7) | 84.6
(29.2) | 91.0
(32.8) | 91.9
(33.3) | 94.7
(34.8) | 96.1
(35.6) | 90.9
(32.7) | 83.1
(28.4) | 72.1
(22.3) | 100.3
(37.9) |
| Mean daily maximum °F (°C) | 59.8
(15.4) | 59.5
(15.3) | 62.3
(16.8) | 64.9
(18.3) | 69.3
(20.7) | 72.9
(22.7) | 75.0
(23.9) | 77.3
(25.2) | 78.2
(25.7) | 74.0
(23.3) | 65.6
(18.7) | 58.9
(14.9) | 68.1
(20.1) |
| Daily mean °F (°C) | 53.2
(11.8) | 52.4
(11.3) | 54.6
(12.6) | 56.2
(13.4) | 60.5
(15.8) | 63.9
(17.7) | 66.1
(18.9) | 67.8
(19.9) | 69.1
(20.6) | 65.1
(18.4) | 58.0
(14.4) | 52.4
(11.3) | 59.9
(15.5) |
| Mean daily minimum °F (°C) | 46.5
(8.1) | 45.3
(7.4) | 46.9
(8.3) | 47.4
(8.6) | 51.6
(10.9) | 54.9
(12.7) | 57.1
(13.9) | 58.3
(14.6) | 60.0
(15.6) | 54.3
(12.4) | 50.3
(10.2) | 45.8
(7.7) | 51.5
(10.9) |
| Mean minimum °F (°C) | 36.5
(2.5) | 34.5
(1.4) | 36.4
(2.4) | 37.3
(2.9) | 41.3
(5.2) | 44.7
(7.1) | 47.3
(8.5) | 48.2
(9.0) | 46.9
(8.3) | 46.4
(8.0) | 40.0
(4.4) | 35.5
(1.9) | 32.4
(0.2) |
| Record low °F (°C) | 28
(−2) | 25
(−4) | 32
(0) | 34
(1) | 38
(3) | 42
(6) | 45
(7) | 46
(8) | 42
(6) | 42
(6) | 32
(0) | 32
(0) | 25
(−4) |
| Average precipitation inches (mm) | 5.96
(151) | 6.15
(156) | 4.80
(122) | 2.00
(51) | 0.71
(18) | 0.06
(1.5) | 0.08
(2.0) | 0.01
(0.25) | 0.07
(1.8) | 1.11
(28) | 2.34
(59) | 6.05
(154) | 29.34
(744.55) |
| Average precipitation days (≥ 0.01 in) | 7.6 | 8.9 | 7.3 | 5.2 | 2.4 | 0.3 | 0.2 | 0.2 | 0.5 | 3.3 | 4.6 | 8.4 | 48.9 |
| Source 1: NOAA | | | | | | | | | | | | | |
| Source 2: National Weather Service (mean maxima/minima 20062020) | | | | | | | | | | | | | |

## Demographics

Historical population
| Census | Pop. | Note |  |
| --- | --- | --- | --- |
| 2010 | 462 |  |  |
| 2020 | 445 |  | −3.7% |
| U.S. Decennial Census | | | |

For statistical purposes, the United States Census Bureau has defined San Simeon as a census-designated place (CDP). The 2010 United States Census reported that San Simeon had a population of 462. The population density was 579.9 inhabitants per square mile (223.9/km2). The racial makeup of San Simeon was 58.4% White, 0.9% African American, 1.1% Native American, 1.9% Asian, 0.4% Pacific Islander, 34.6% from other races, and 2.6% from two or more races. Hispanics or Latinos of any race were 55.8%.

Of the 197 households, 26.9% had children under the age of 18 living in them, 47.7% were married couples living together, 7.1% had a female householder with no husband present 6.6% had a male householder with no wife present, 6.1% were unmarried opposite-sex partnerships, and 2.5% were same-sex married couples or partnerships; 34.0% of the households were made up of individuals, and 15.2% had someone living alone who was 65 years of age or older. The average household size was 2.34. About 61.4% of all households were families; the average family size was 3.00.

The population was distributed as 22.9% under the age of 18, 6.7% aged 18 to 24, 24.2% aged 25 to 44, 28.1% aged 45 to 64, and 18.0% who were 65 years of age or older. The median age was 40.7 years. For every 100 females, there were 105.3 males. For every 100 females age 18 and over, there were 102.3 males.

The 301 housing units averaged 377.8 per square mile (145.9/km2), of which 44.2% were owner-occupied, and 55.8% were occupied by renters. The homeowner vacancy rate was 2.2%; the rental vacancy rate was 11.3%; 31.0% of the population lived in owner-occupied housing units and 68.8% lived in rental housing units.

## Infrastructure

The San Simeon Community Services District provides water and sewerage. The wastewater treatment plant is operated by a private company under contract with the district. The facility also processes sewage for Hearst Castle.

## InfoBox

| San Simeon | |
| --- | --- |
| Unincorporated community
Census-designated place | |
| View of Hearst Castle | |
| San SimeonLocation within the state of CaliforniaSan SimeonSan Simeon (the United States) | |
| Coordinates: 35°38′38″N 121°11′23″W / 35.64389°N 121.18972°W / 35.64389; -121.18972 | |
| Country | United States |
| State | California |
| County | San Luis Obispo |
| Area | |
| Total | 0.797 sq mi (2.063 km2) |
| Land | 0.797 sq mi (2.063 km2) |
| Water | 0 sq mi (0 km2)  0% |
| Elevation | 230 ft (70 m) |
| Population (2020) | |
| Total | 445 |
| Density | 560/sq mi (220/km2) |
| Time zone | UTC-8 (Pacific (PST)) |
| Summer (DST) | UTC-7 (PDT) |
| ZIP codes | 93452 |
| Area code | 805 |
| GNIS feature ID | 248966 |


title: Piano Vetrale

abstract: Piano Vetrale, also shortened as Vetrale or Piano, is a southern Italian village and hamlet (frazione) of Orria, a municipality in the province of Salerno, Campania. As of 2011, its population was of 475.

text:
# Piano Vetrale

**Piano Vetrale**, also shortened as **Vetrale** or **Piano**, is a southern Italian village and hamlet (*frazione*) of Orria, a municipality in the province of Salerno, Campania. As of 2011, its population was of 475.

## History

The origin of the toponym comes from *Planus* (referred to the high plain in which it lies) and *Veteres* (referred to its founders, some veterans of the Roman army from Gioi). The village, originally named *Piano del Cilento*, is part of the municipality of Orria since 1801 and was divided into two separated settlements (***Piano*** and ***Vetrale***) until the 1960s.

## Culture

Piano Vetrale became a "painted town" with large *murales* outside the houses, at the end of the 1970s, following the idea of the Sicilian artist Pino Crisanti.

## Geography

Located in the middle of Cilento and transcluded into its national park, Piano Vetrale is a hill village that spans on a ridge upon the valley of Alento river's source. It is divided into the quarters of Piano (west) and Vetrale (east), contiguous and divided by a little valley, named *Vallone di Sabato*.

Piano Vetrale lies between Orria (3.5 km west), Gioi (4 km southeast) and Stio (6.5 km east), and is connected to them by the provincial road SP56/B. The village is 7.3 km far from Perito, 7.7 from Ostigliano, 8 from Gorga, 9 from Cardile, 10 from Casino Lebano (the other hamlet of Orria), and 17 from Vallo della Lucania.

## Main sights

* St. Sophia's Church and its bell tower
* The *murales* within the village

## Personalities

Media related to **Piano Vetrale** at Wikimedia Commons

## InfoBox

| Piano Vetrale | |
| --- | --- |
| *Frazione* | |
| OSM map of Piano Vetrale | |
| Piano VetraleLocation of Piano Vetrale in Italy | |
| Coordinates: 40°18′15.9″N 15°12′04.1″E / 40.304417°N 15.201139°E / 40.304417; 15.201139 | |
| Country | Italy |
| Region | Campania |
| Province | Salerno (SA) |
| *Comune* | Orria |
| Elevation | 575 m (1,886 ft) |
| Population (2011) | |
| Total | 475 |
| Demonym | *Pianesi / Vetralesi* |
| Time zone | UTC+1 (CET) |
| Summer (DST) | UTC+2 (CEST) |
| Postal code | 84060 |
| Dialing code | (+39) 0974 |
| Patron saint | St. Elias |
| Saint day | Last sunday of July |


abstract: Senior societies at University of Pennsylvania are an important part of student life.

text:
# University of Pennsylvania senior societies

**Senior societies at University of Pennsylvania** are an important part of student life.

## Activity-based

### Bell Senior Society

The Bell Senior Society was founded in 2014. The organization brings together students involved with innovation and technology around Penn's campus. New members are selected by the previous class based on potential, and passion for technology and entrepreneurship.

### Kinoki Senior Society

Kinoki was founded in the spring of 2014. This organization brings together students who plan on pursuing careers in the film and entertainment industry.

### Omega Honor Society

The Zeta Xi Chapter of the Order of Omega was rechartered at Penn in 2014. Unlike its "Omega" counterpart below, the chapter has both a university affiliation with the Office of Fraternity and Sorority Life, and a national affiliation. Omega is composed of juniors and seniors who best represent the positive aspects of Greek life: character, scholarship, service, and leadership.

### The Order Senior Society

The Order Senior Honor Society, exists to recognize distinguished and diverse leaders in the Greek community. It is composed of influential members of Greek organizations and other similar student groups (colloquially known as "off-campus fraternities/sororities").

### Osiris Senior Society

Osiris, founded in the spring of 2013 by Lainie Huston and Jackson Foster, brings together senior leaders and outstanding members of the performing arts community. The society draws its name from the god Osiris, who was believed by some in ancient Greco-Egyptian times to have been the god who brought together the nine muses. Similarly, the society provides a forum for students of different art forms, including vocal, dance, theatrical, instrumental, photographic, and tech among others, to strengthen ties across the performing arts community. Throughout the year, members attend social events and support each other at shows, and each May members perform a senior showcase highlighting the talents of these students and fostering collaborative performance.

### Caduceus Society

Founded by a group of premedical students, this invite-only society seeks to identify the most promising physicians of tomorrow. The society's motto, "Quoquo Modo Necessarium," translates to "By any means necessary." This adage reflects the members' unyielding commitment to the pursuit of medical knowledge and their readiness to transcend traditional boundaries in search of excellence. Members of this society demonstrate not only exceptional academic achievements but also a deep commitment to the pioneering edges of medical science and ethical practice.

## Identity-based

### Atlas Senior Society

The Atlas Society was founded in 2016 by five international students. Atlas strives to create an ethnically and culturally diverse community of international students who have demonstrated leadership and an interest in intercultural learning and global experiences. The founding class includes 21 members from 18 countries and territories.

### Carriage Senior Society

The Carriage Senior Society, founded in the spring of 2013, is a senior honor society of leaders from around campus who are members of the LGBTQ+ community. It is named for the home of the university's LGBT Center, Carriage House. Their symbol is a twelve-spoked carriage wheel and members refer to themselves as "Spokes."

New members are added both as Juniors in their spring semester and as Seniors in their fall semester. While members continue the traditional tap system for potential applicants, in recent years an open invitation to the informational "Smoker" has been distributed to LGBTQ groups on campus. Any eligible student who attends the Smoker is then welcome to apply whether or not they have been tapped. An effort is made to include a diversity of identities and areas of leadership on campus in each class.

### Cipactli Latino Honor Society

The Cipactli Latino Honor Society was founded in 2001. The mission and purpose of Cipactli is to acknowledge individual academic achievement, leadership, and distinguished service to the Latino community. Cipactli is the only Latino honor society in the Ivy League.

The members of Cipactli are chosen anytime between their junior fall semester and senior fall semester, and go through a rigorous application process. They are chosen for their outstanding work both in and outside the academic sphere, as well as their deep commitment to helping their communities develop in a sustainable and meaningful way. Cipactli's philosophy is known as "The three pillars of Cipactli", which are Leadership, Academic Achievement, and Community Service.

### Onyx Senior Society

The Onyx Senior Society was founded in 1974. With the aid of administrators Provost Elliot, Alice E. Emerson (Dean of Students), and Harold Haskins (Dean of Students), the honor society to encourages high academic achievement and community service at the university. The society recognizes outstanding performance within, and outside of, the classroom. The organization plays a significant role in promoting the academic success of minority students who operate in a competitive environment.

One of the goals of Onyx was to re-establish the Society for African-American Students at the University of Pennsylvania. The society provided an all-expenses-paid program for black students in the summer before their first year. The program lasted from 1969 to 1972, and concentrated on preparing its participants for the academic mainstream by providing books, room and board, a stipend, and two credited courses. This program later birthed the Pre-Freshman Program. In response to such changes, the goals of Onyx have also changed and developed over time. In the past, Onyx has focused on forums as a means to inform the campus community about black issues. Forum topics have included the organization and promotion of networking within the black community, and mentoring, both on campus and in the surrounding Philadelphia community. Onyx hopes to create a positive social experience for blacks at the university, and to recognize black achievement, past and present. Notable members of Onyx include Grammy Award-winning singer John "Legend" Stephens, former U.S. Congressman Harold Ford Jr., and former mayor of New Orleans and current National Urban League President and CEO, Marc Morial.

### Oracle Senior Honor Society

The Oracle Senior Honor Society was founded in the fall of 2002. It recognizes outstanding members of each senior class who demonstrate passion, leadership, commitment and achievement as a student of Asian Pacific heritage or for the Asian Pacific community at the University of Pennsylvania. Since its founding, Oracle has represented leadership from organizations that span all facets of university life, from academics and service organizations, to cultural and performing arts groups, to Greek life and student government.

As a self-perpetuating senior society, juniors have the opportunity to apply for the society in the spring, and seniors have the opportunity to apply in the fall. Potential members, all of whom have served the university in some leadership capacity, learn more about the society and to meet the current members at an informal smoker. Each prospective member must then submit a written application detailing their qualifications. The current senior class selects the new class of Oracle members, representative of the diverse student population, by selecting from the applicant pool based on their fit to Oracle's purpose of demonstrating passion, leadership, commitment, and achievement.

### Shamash Senior Society

Shamash Senior Society was founded in April 2018 in order to celebrate and create a community surrounding Jewish students on Penn's campus. The group aims to bring together leaders of the Jewish community and those that have established a commitment to leadership across campus that have a connection to Judaism. Shamash rests on four core tenets: impact, community, diversity, and service, and members are expected to uphold these tenets to the best of their ability.

The name of the society comes from the Hebrew word for "servant" or "attendant", and is more commonly known as the "helper" candle on the Hanukkah menorah. This symbolism reflects a connection between leadership and Judaism that underscores the mission of the society.

Shamash is composed of members of the graduating class of seniors. Potential new members are invited to apply at the end of their junior year for membership in the following year's class, as well as eligible to apply in the fall of their senior year as well.

## School-based

### Hexagon Senior Society

Hexagon is the oldest school-based senior honor society at the University of Pennsylvania. The society was founded in 1910 to promote fraternization across different engineering majors and recognize outstanding leaders in the School of Engineering and Applied Sciences. Members often lead tours of the Engineering School buildings. Hexagon members are selected based on outstanding achievements in scholarship, leadership, and service.

### Snakes Senior Society

The Snakes Society was founded in 1993. It is a senior society that is devoted to assemble a diverse group of outstanding Wharton undergraduates who have excelled academically, distinguished themselves as leaders among their peers, and contributed to the well-being of the community.

### Nightingales Senior Society

The Nightingales Senior Society was founded in 2011. It is a society dedicated to senior nurses who have demonstrated leadership in the nursing school.

### Gryphon Senior Society

The Gryphon Senior Society was founded in 2020. It is a society dedicated to recognizing outstanding student leaders in the College of Arts and Sciences.

## Traditional societies

These were the first senior societies to be created at the University of Pennsylvania. The three traditional societies are Friars, Sphinx, and Mortarboard. Friars and Sphinx explicitly seek campus leaders, while Mortarboard seeks to recognize "achievements in scholarship, leadership, and service." Friars and Sphinx are exclusive to the University of Pennsylvania, whereas Mortarboard is a national honor society.

### Friars Senior Society

Founded in 1899, Friars Senior Society is the oldest and most active undergraduate senior honor society at the University of Pennsylvania with over 2,100 alumni in the United States and in 23 countries throughout the world. Friars was formed to establish uncompromising democracy in university activities. Each class is composed of one-third athletic captains, one-third performing arts leaders, and one-third student government, Greek, publications and community service leaders. Friars promotes interaction between those from all walks of life who have given their time and energies to making the university what it is; hence the name Friars, for those who sacrifice their time during college to meaningful activities. Throughout Penn's history, society members have contributed to many aspects of Penn life, such as the addition of straw hats to Hey Day in 1949, the Penn mascot in 1964 and the creation of Spring Fling in 1975.

### Mortar Board Senior Society

Mortar Board is a chapter of the national Mortar Board Senior Honor Society. It was the first and only senior society open to women until 1971, when Sphinx and Friars became co-ed. Mortar Board recognizes juniors and seniors for their achievement.

### Sphinx Senior Society

The Sphinx Senior Society at the University of Pennsylvania, founded in 1900, is one of the most well-known honor societies at Penn, recognizing the top seniors who have made significant contributions to the university as leaders of the campus. Continuing in this tradition, the society has come to represent all facets of university life and has reflected the changing face of Penn's student body. Members today include leaders in student government, performing arts, media, service groups, cultural organizations, Greek life, athletics, and other realms of student affairs. Sphinx was the first senior society at Penn to admit African-Americans, doing so in 1952, and in February 1971 was the first to be co-ed.

### Philomathean Society

Penn's oldest society, The Philomathean Society, was founded in 1813, and is one of the United States' oldest collegiate literary societies. It continues to host lectures and intellectual events open to the public.

### Zelosophic Society

The Zelosophic Society, one of the two oldest senior societies at the University of Pennsylvania, was founded in 1829 as an alternative to its rival literary society, Philomathean Society (which was established 1813). Per Penn archives, “Zelosophic” is translated roughly as “endowed with a zeal for learning or wisdom” and its members were commonly called “Zelos”. The society's purpose was to discuss literature and, like the Philomathean, to conduct debates. Per Penn archives, the Zelosophic Society's first two iterations lasted from 1829 to 1864 and again from 1892 to 1941.

1. "Office of Student Affairs at the University of Pennsylvania". Archived from the original on December 28, 2010. Retrieved September 23, 2010.
2. Finkelstein, Morgan (April 8, 2010). "Oh, Look, Senior Societies". *Under the Button*. Archived from the original on November 29, 2010.
3. Pollock, Judy (April 15, 2008). "The Daily Pennsylvanian". *Thedp.com*. Archived from the original on June 24, 2016. Retrieved May 29, 2016.
4. "Constitution and Bylaws : Order of Omega". *orderofomega.org*. Archived from the original on 2016-04-04. Retrieved 2016-04-05.
5. Osiris Senior Society Archived April 7, 2014, at the Wayback Machine
6. "Cipactli Latino Honor Society". Archived from the original on 2015-02-16. Retrieved 2014-03-31.
7. About Oracle Archived 2012-07-28 at the Wayback Machine Oracle Senior Honor Society
8. Archived 2012-07-19 at the Wayback Machine Oracle Senior Society
9. Spring Senior Societies, Round Two Archived 2012-04-13 at the Wayback Machine Under the Button - April 9, 2012
10. "Shamash Senior Society". *shamashseniorsociety.org*. Archived from the original on 2018-09-21. Retrieved 2018-09-21.
11. "About Mortar Board". *Penn Mortar Board*. Archived from the original on 2 February 2015. Retrieved 6 October 2014.
12. Tamblin C. Smith; et al. (1948). *Pennsylvania Pictures, January 1948 Vol. IV, No. 3*. Franklin Society Publication. pp. 3, . Archived from the original on 2015-12-26. Retrieved 2015-10-17.
13. http://www.archives.upenn.edu/histy/features/traditions/heyday/timeline.htm%5B%5D
14. Tamblin C. Smith; et al. (1948). *Pennsylvania Pictures, January 1948 Vol. IV, No. 3*. Franklin Society Publication. pp. 4, . Archived from the original on 2015-12-26. Retrieved 2015-10-17.
15. Compiled by W.J. Maxwell (1917). *General alumni catalogue of the University of Pennsylvania*. University of Pennsylvania. p. 1336. Archived from the original on 2017-08-10. Retrieved 2017-02-08.
16. University of Pennsylvania (1900). *The Record* (PDF). Class of 1900. p. 377. Archived (PDF) from the original on 2016-03-22. Retrieved 2017-02-08.
17. Tamblin C. Smith; et al. (1948). *Pennsylvania Pictures, January 1948 Vol. IV, No. 3*. Franklin Society Publication. p. 3. Archived from the original on 2015-12-26. Retrieved 2015-10-17.
18. NEGROES ELECTED TO SPHINX AT U.OF P|New York Times, May 24, 1952\>
19. Male Honor Society at Penn Planning to Admit Women||New York Times, February 07, 1971\>
20. Philomathean Society (1913). *A History of the Philomathean Society of the University of Pennsylvania*. Philadelphia: University of Pennsylvania. p. 22. Retrieved November 5, 2015.
21. "Zelosophic Society of the University of Pennsylvania Records". *archives.upenn.edu*. Retrieved November 28, 2021.


title: San Ferdinando (church), Naples

abstract: The Church of San Ferdinando is a historic church located on the Piazza Triesti e Trento, near the Royal Palace of Naples, in central Naples, Italy.

text:
# San Ferdinando (church), Naples

The Church of **San Ferdinando** is a historic church located on the Piazza Triesti e Trento, near the Royal Palace of Naples, in central Naples, Italy.

## History

The original church at the site was dedicated by the Jesuits to Saint Francis Xavier, and was built in 1636. Reconstruction in mid 1650s was entrusted to Cosimo Fanzago. In 1767, with the expulsion of the Jesuits from the realm, the church was granted to the Sacred Military Constantinian Order of Saint George who dedicated the church to Saint Ferdinand III of Castile, the patron saint of the reigning king of Naples Ferdinand IV.

The vault has a fresco with the story of Saint Francis Xavier and other Jesuits by Paolo De Matteis. The church contains statues by Domenico Antonio Vaccaro and Giuseppe Sanmartino. The main altarpiece is a canvas depicting *San Ferdinando* by Federico Maldarelli.

## InfoBox

| Church of San Ferdinando | |
| --- | --- |
| Chiesa di San Ferdinando | |
| The Church of San Ferdinando in Naples . | |
|  | |
| 40°50′15″N 14°14′55″E / 40.83762°N 14.248736°E / 40.83762; 14.248736 | |
| Location | Piazza Trieste e Trento
Naples
Province of Naples, Campania |
| Country | Italy |
| Denomination | Roman Catholic |
| History | |
| Status | Active |
| Architecture | |
| Architectural type | Baroque architecture |
| Groundbreaking | 1636 |
| Completed | 1759 |
| Administration | |
| Diocese | Roman Catholic Archdiocese of Naples |


title: Cardinal function

abstract: In mathematics, a cardinal function is a function that returns cardinal numbers.

text:
# Cardinal function

In mathematics, a **cardinal function** (or **cardinal invariant**) is a function that returns cardinal numbers.

## Cardinal functions in set theory

$\rm {add}(I)=\min\\{|{\mathcal {A}|:{\mathcal {A}\subseteq I\wedge \bigcup {\mathcal {A}\notin I\\}.}}}$ The "additivity" of *I* is the smallest number of sets from *I* whose union is not in *I* any more. As any ideal is closed under finite unions, this number is always at least $\aleph \_{0}$; if *I* is a σ-ideal, then $\operatorname {add} (I)\geq \aleph \_{1}.$ $\operatorname {cov} (I)=\min\\{|{\mathcal {A}|:{\mathcal {A}\subseteq I\wedge \bigcup {\mathcal {A}=X\\}.}}}$ The "covering number" of *I* is the smallest number of sets from *I* whose union is all of *X*. As *X* itself is not in *I*, we must have add(*I*) ≤ cov(*I*). $\operatorname {non} (I)=\min\\{|A|:A\subseteq X\ \wedge \ A\notin I\\},$ The "uniformity number" of *I* (sometimes also written $\rm {unif}(I)$) is the size of the smallest set not in *I*. Assuming *I* contains all singletons, add(*I*) ≤ non(*I*). $\rm {cof}(I)=\min\\{|{\mathcal {B}|:{\mathcal {B}\subseteq I\wedge \forall A\in I(\exists B\in {\mathcal {B})(A\subseteq B)\\}.}}}$ The "cofinality" of *I* is the cofinality of the partial order (*I*, ). It is easy to see that we must have non(*I*) ≤ cof(*I*) and cov(*I*) ≤ cof(*I*). In the case that $I$ is an ideal closely related to the structure of the reals, such as the ideal of Lebesgue null sets or the ideal of meagre sets, these cardinal invariants are referred to as cardinal characteristics of the continuum. * For a preordered set $(\mathbb {P} ,\sqsubseteq )$ the **bounding number** $\mathfrak {b}(\mathbb {P} )$ and **dominating number** $\mathfrak {d}(\mathbb {P} )$ are defined as

$$\mathfrak {b}(\mathbb {P} )=\min {\big \\{}|Y|:Y\subseteq \mathbb {P} \ \wedge \ (\forall x\in \mathbb {P} )(\exists y\in Y)(y\not \sqsubseteq x){\big \\},}$$

$\mathfrak {d}(\mathbb {P} )=\min {\big \\{}|Y|:Y\subseteq \mathbb {P} \ \wedge \ (\forall x\in \mathbb {P} )(\exists y\in Y)(x\sqsubseteq y){\big \\}.}$ * In PCF theory the cardinal function $pp\_{\kappa }(\lambda )$ is used.

## Cardinal functions in topology

Cardinal functions are widely used in topology as a tool for describing various topological properties. Below are some examples. (Note: some authors, arguing that "there are no finite cardinal numbers in general topology", prefer to define the cardinal functions listed below so that they never taken on finite cardinal numbers as values; this requires modifying some of the definitions given below, for example by adding " $\\;\\;+\\;\aleph \_{0}$" to the right-hand side of the definitions, etc.)

* Perhaps the simplest cardinal invariants of a topological space $X$ are its cardinality and the cardinality of its topology, denoted respectively by $|X|$ and $o(X).$
* The **weight** $\operatorname {w} (X)$ of a topological space $X$ is the cardinality of the smallest base for $X.$ When $\operatorname {w} (X)=\aleph \_{0}$ the space $X$ is said to be *second countable*.
    + The **$\pi $-weight** of a space $X$ is the cardinality of the smallest $\pi $-base for $X.$ (A $\pi $-base is a set of non-empty open sets whose supersets includes all opens.)
    + The **network weight** $\operatorname {nw} (X)$ of $X$ is the smallest cardinality of a network for $X.$ A *network* is a family $\mathcal {N}$ of sets, for which, for all points $x$ and open neighbourhoods $U$ containing $x,$ there exists $B$ in $\mathcal {N}$ for which $x\in B\subseteq U.$
* The **character** of a topological space $X$ **at a point** $x$ is the cardinality of the smallest local base for $x.$ The **character** of space $X$ is $\chi (X)=\sup \\;\\{\chi (x,X):x\in X\\}.$ When $\chi (X)=\aleph \_{0}$ the space $X$ is said to be *first countable*.
* The **density** $\operatorname {d} (X)$ of a space $X$ is the cardinality of the smallest dense subset of $X.$ When $\rm {{d}(X)=\aleph \_{0}}$ the space $X$ is said to be *separable*.
* The **Lindelöf number** $\operatorname {L} (X)$ of a space $X$ is the smallest infinite cardinality such that every open cover has a subcover of cardinality no more than $\operatorname {L} (X).$ When $\rm {{L}(X)=\aleph \_{0}}$ the space $X$ is said to be a *Lindelöf space*.
* The **cellularity** or **Suslin number** of a space $X$ is

$$\operatorname {c} (X)=\sup\\{|{\mathcal {U}|:{\mathcal {U}{\text{ is a family of mutually disjoint non-empty open subsets of }X\\}.}}}$$

* The **hereditary cellularity** (sometimes called **spread**) is the least upper bound of cellularities of its subsets: $s(X)={\rm {hc}(X)=\sup\\{{\rm {c}(Y):Y\subseteq X\\}}}$ or $s(X)=\sup\\{|Y|:Y\subseteq X{\text{ with the subspace topology is discrete}\\}}$ where "discrete" means that it is a discrete topological space.
* The **extent** of a space $X$ is $e(X)=\sup\\{|Y|:Y\subseteq X{\text{ is closed and discrete}\\}.}$ So $X$ has countable extent exactly when it has no uncountable closed discrete subset.
* The **tightness** $t(x,X)$ of a topological space $X$ **at a point** $x\in X$ is the smallest cardinal number $\alpha $ such that, whenever $x\in {\rm {cl}\_{X}(Y)}$ for some subset $Y$ of $X,$ there exists a subset $Z$ of $Y$ with $|Z|\leq \alpha ,$ such that $x\in \operatorname {cl} \_{X}(Z).$ Symbolically, $t(x,X)=\sup \left\\{\min\\{|Z|:Z\subseteq Y\ \wedge \ x\in {\rm {cl}\_{X}(Z)\\}:Y\subseteq X\ \wedge \ x\in {\rm {cl}\_{X}(Y)\right\\}.}}$ The **tightness of a space** $X$ is $t(X)=\sup\\{t(x,X):x\in X\\}.$ When $t(X)=\aleph \_{0}$ the space $X$ is said to be *countably generated* or *countably tight*.
    + The **augmented tightness** of a space $X,$ $t^{+}(X)$ is the smallest regular cardinal $\alpha $ such that for any $Y\subseteq X,$ $x\in {\rm {cl}\_{X}(Y)}$ there is a subset $Z$ of $Y$ with cardinality less than $\alpha ,$ such that $x\in {\rm {cl}\_{X}(Z).}$

### Basic inequalities

$c(X)\leq d(X)\leq w(X)\leq o(X)\leq 2^{|X|}$ $e(X)\leq s(X)$ $\chi (X)\leq w(X)$ $\operatorname {nw} (X)\leq w(X){\text{ and }o(X)\leq 2^{\operatorname {nw} (X)}}$

## Cardinal functions in Boolean algebras

Cardinal functions are often used in the study of Boolean algebras. We can mention, for example, the following functions:

* **Cellularity** $c(\mathbb {B} )$ of a Boolean algebra $\mathbb {B} $ is the supremum of the cardinalities of antichains in $\mathbb {B} $.
* **Length** $\rm {length}(\mathbb {B} )$ of a Boolean algebra $\mathbb {B} $ is

$$\rm {length}(\mathbb {B} )=\sup {\big \\{}|A|:A\subseteq \mathbb {B} {\text{ is a chain}{\big \\}}}$$

* **Depth** $\rm {depth}(\mathbb {B} )$ of a Boolean algebra $\mathbb {B} $ is

$\rm {depth}(\mathbb {B} )=\sup {\big \\{}|A|:A\subseteq \mathbb {B} {\text{ is a well-ordered subset}{\big \\}}}$. * **Incomparability** $\rm {Inc}(\mathbb {B} )$ of a Boolean algebra $\mathbb {B} $ is

$\rm {Inc}({\mathbb {B} })=\sup {\big \\{}|A|:A\subseteq \mathbb {B} {\text{ such that }\forall a,b\in A{\big (}a\neq b\ \Rightarrow \neg (a\leq b\ \vee \ b\leq a){\big )}{\big \\}}}$. * **Pseudo-weight** $\pi (\mathbb {B} )$ of a Boolean algebra $\mathbb {B} $ is

$$\pi (\mathbb {B} )=\min {\big \\{}|A|:A\subseteq \mathbb {B} \setminus \\{0\\}{\text{ such that }\forall b\in B\setminus \\{0\\}{\big (}\exists a\in A{\big )}{\big (}a\leq b{\big )}{\big \\}.}}$$

## Cardinal functions in algebra

Examples of cardinal functions in algebra are:

* A Glossary of Definitions from General Topology


title: Ram Mohan P.

abstract: Ram Mohan Paruvu is an Indian film screenwriter, producer, and director known for his works in Telugu cinema. He owns the production house Sunshine Cinemas.

text:
# Ram Mohan P.

**Ram Mohan Paruvu** (born 21 May 1969) is an Indian film screenwriter, producer, and director known for his works in Telugu cinema. He owns the production house Sunshine Cinemas.

## Career

The first film under the Sunshine Cinemas banner is Ram's 2013 film *Uyyala Jampala*.

## Filmography

| Year | Title | Director | Producer | Writer |
| --- | --- | --- | --- | --- |
| 2008 | *Ashta Chamma* |  | Yes |  |
| 2011 | *Golconda High School* |  | Yes |  |
| 2013 | *Uyyala Jampala* |  | Yes | Yes |
| 2015 | *Thanu Nenu* | Yes | Yes |  |
| 2016 | *Soggade Chinni Nayana* |  |  | Story |
| 2016 | *Pittagoda* |  | Yes |  |
|

## Personal life

His brother Harimohan Paruvu is an English writer.

### Awards and nominations

## InfoBox

| Ram Mohan P. | |
| --- | --- |
| Born | (1969-05-21) 21 May 1969 |
| Nationality | Indian |
| Other names | Ram Mohan |
| Occupations |  |
| Known for | Telugu Films |
| Notable work | *Uyyala Jampala* (2013) |


title: Caelostomus perrieri

abstract: Caelostomus perrieri is a species in the ground beetle family Carabidae. It is found in Madagascar.

text:
# Caelostomus perrieri

***Caelostomus perrieri*** is a species in the ground beetle family Carabidae. It is found in Madagascar.

## InfoBox

| *Caelostomus perrieri* | |
| --- | --- |
|
| Scientific classification | |
| Domain: | Eukaryota |
| Kingdom: | Animalia |
| Phylum: | Arthropoda |
| Class: | Insecta |
| Order: | Coleoptera |
| Family: | Carabidae |
| Subfamily: | Pterostichinae |
| Genus: | *Caelostomus* |
| Species: | ***C. perrieri*** |
| Binomial name | |
| ***Caelostomus perrieri***<br>Jeannel, 1948 | |
|


title: Turbonilla aepynota

abstract: Turbonilla aepynota is a species of sea snail, a marine gastropod mollusk in the family Pyramidellidae, the pyrams and their allies.

text:
# Turbonilla aepynota

***Turbonilla aepynota*** is a species of sea snail, a marine gastropod mollusk in the family Pyramidellidae, the pyrams and their allies.

## Description

The small, diaphanous shell has an elongate-conic shape. Its length measures 3.2 mm. The 2½ whorls of the protoconch are small and helicoid. They form a moderately elevated spire, with their axis at right angles to that of the succeeding turns, in the first of which they are about one-fifth immersed. The eight whorls of the teleoconch are situated high between the sutures. They are very strongly shouldered at the summits, somewhat contracted at the periphery, and well rounded. They are marked by strong, sublamellar axial ribs that render the summits strongly crenulate. Sixteen of the axial ribs appear upon the first and second, 18 upon the third, fourth, and fifth, and 20 upon the remaining turns. The intercostal spaces a little wider than the ribs, deeply sunk below the general surface, and extend to the suture on all the turns of the spire. The sutures are strongly marked. The periphery of the body whorl is feebly angulated. The base of the shell is short, well rounded, and smooth. The aperture is rather large, and subquadrate. The posterior angle is obtuse. The outer lip is thin. It isbent abruptly anteriorly toward the columella, which it joins almost at right angles. The columella is very slender and gently curved.

## Distribution

The type specimen was found in the Pacific Ocean off San Pedro, Baja California.

## InfoBox

| *Turbonilla aepynota* | |
| --- | --- |
|  | |
| Drawing of a shell of *Turbonilla aepynota* | |
|
| Scientific classification | |
| Domain: | Eukaryota |
| Kingdom: | Animalia |
| Phylum: | Mollusca |
| Class: | Gastropoda |
| Family: | Pyramidellidae |
| Genus: | *Turbonilla* |
| Species: | ***T. aepynota*** |
| Binomial name | |
| ***Turbonilla aepynota***<br>Dall & Bartsch, 1909 | |
|
| Synonyms | |
| *Turbonilla (Chemnitzia) aepynota* Dall & Bartsch, 1909 | |


title: Studio Comet

abstract: Studio Comet Co., Ltd. is an animation studio with its headquarters in Toyotamanaka, Nerima, Tokyo, Japan. It was established on January 21, 1986.

text:
# Studio Comet

**Studio Comet Co., Ltd.** (Japanese: 株式会社スタジオコメット, Hepburn: *Kabushiki Kaisha Sutajio Kometto*) is an animation studio with its headquarters in Toyotamanaka, Nerima, Tokyo, Japan. It was established on January 21, 1986.

## Notable staff

* Hiroshi Kanazawa (animation director, character designer)
* Kazuo Harada (animation producer, sound effects and audio director)
* Shin Misawa (animation)

## Productions

| Title | Media type | Run dates |
| --- | --- | --- |
| *A Salad Bowl of Eccentrics* | TV series | 2024; with SynergySP |
| *Art of Fighting* | OVA | 1993 |
| *Baby Princess 3D Paradise Love* | OVA | 2011 |
| *Fatal Fury: Legend of the Hungry Wolf* | TV special | 1992 |
| *Bikkuriman 2000* | first digital production, TV series | 2000 |
| *Bowwow Celebrity Poodle Let's Go! Tetsunoshin* | TV series | 2006 |
| *Capeta* | TV series | 2005–2006 |
| *Captain Tsubasa J* | TV series | 1994–1995 |
| *Fatal Fury 2: The New Battle* | TV special | 1993 |
| *Chō Hatsumei Boy Kanipan* | TV series | 1999 |
| *Cute High Earth Defense Club LOVE! LOVE!* | TV series | 2016 |
| *Cute High Earth Defense Club HAPPY KISS!* | TV series | 2018 |
| *Dragon Quest* | TV series | 1989–1991 |
| *Dr. Rin ni Kiitemite!* | TV series | 2001 |
| *Fairy Ranmaru* | TV series | 2021 |
| *Hatsumei Boy Kanipan* | TV series | 1998 |
| *Highschool! Kimengumi* | TV series (from ep.9, working with Gallop) | 1985–1987 |
| *High School Mystery: Gakuen Nanafushigi* | TV series | 1991 |
| *Humanoid Monster Bem* | TV series | 2006 |
| *Initial D* | TV series | 1998; with Studio Gallop on behalf of Pastel |
| *Kirby of the Stars* | TV series | 2003; with Studio Sign and Warpstar, Inc. |
| *Jewelpet* | TV series | 2009 |
| *Jewelpet Twinkle☆* | TV series | 2010 |
| *Jewelpet Sunshine* | TV series | 2011 |
| *Jewelpet Kira☆Deco* | TV series | 2012 |
| *Jewelpet the Movie: Sweets Dance Princess* | Theatrical film | 2012 |
| *Fatal Fury: The Motion Picture* | Theatrical film | 1994 |
| *Jewelpet Happiness* | TV series | 2013 |
| *Lady Jewelpet* | TV series | 2014–2015; with Zexcs |
| *Kero Kero Chime* | TV series | 1997 |
| *Maboroshi Mabo-chan* | TV series | 1992 |
| *Meimon! Dai San Yakyūbu* | TV series | 1988–1989 |
| *Mizuiro Jidai* | TV series | 1996 |
| *Mutsuen Meiryū Gaiden: Shura no Toki* | TV series | 2004 |
| *Onegai My Melody* | TV series | 2005 |
| *Onegai My Melody: Kuru Kuru Shuffle* | TV series | 2006 |
| *Onegai My Melody: Sukkiri* | TV series | 2007 |
| *Onegai My Melody: Kirara* | TV series | 2008 |
| *Onegai My Melody: Yū & Ai* | Theatrical film | 2012 |
| *Peach Girl* | TV series | 2005 |
| *Possibly the Greatest Alchemist of All Time* | TV series | 2025 |
| *Reborn to Master the Blade: From Hero-King to Extraordinary Squire* | TV series | 2023 |
| *RobiHachi* | TV series | 2019 |
| *Samurai Shodown* | TV special | 1994; with Studio Gazelle |
| *School Rumble* | TV series | 2004 |
| *School Rumble: Second Term* | TV series | 2006 |
| *Shin Megami Tensei: D-Children – Light and Dark* | TV series (from ep.27) | 2002–2003 |
| *Shōta no Sushi* | TV special | 1999 |
| *Sora no Manimani* | TV series | 2009 |
| *Suzuka* | TV series | 2005 |
| *The Marshmallow Times* | TV series | 2004 |
| *Tsuide ni Tonchinkan* | TV series | 1987–1988 |
| *Tsuyoshi Shikkari Shinasai* | TV series | 1992–1994 |
| *Whistle!* | TV series | 2002 |

## InfoBox

Studio Comet Co., Ltd.
|
|  |
| Company type | Kabushiki gaisha |
| Industry | Japanese TV, movie, and animation studio |
| Founded | 1986<br>Tokyo, Japan |
| Headquarters | Toyotamanaka, Nerima, Tokyo, Japan |
| Website | Studio Comet homepage |


title: Sanmu incident

abstract: The Sanmu incident was an attempted coup d'état in Japan that was foiled on December 12, 1961. During the raid undertaken by the National Police Agency, 13 conspirators were arrested. It was the first coup attempt in post-war Japan. The only other attempt in this period, led by Yukio Mishima, would follow in 1970.

text:
# Sanmu incident

The **Sanmu incident** (三無事件, *San mu jiken*) was an attempted coup d'état in Japan that was foiled on December 12, 1961. During the raid undertaken by the National Police Agency, 13 conspirators were arrested. It was the first coup attempt in post-war Japan. The only other attempt in this period, led by Yukio Mishima, would follow in 1970.

## Incident

The stated goals of the group were to kill Prime Minister Hayato Ikeda, his Cabinet, and take control of the National Diet. They hoped that this would prevent Japan from succumbing to a communist revolution. At the time of the arrest, the conspirators had already come into possession of uniforms and deadly weaponry, such as grenades and rifles.

Amongst the members were officers of the former Imperial Japanese Army, such as Major General Tokutaro Sakurai. Also involved were businessman Toyosaku Kawanami and former Manchukuo minister of economic affairs Han Yunjie. Another participant was Mikami Taku, a former Navy Lieutenant. He had previously been involved in a pre-war coup attempt in 1932, known as the May 15 incident, for which he was then imprisoned.


title: Bounded set (topological vector space)

abstract: In functional analysis and related areas of mathematics, a set in a topological vector space is called bounded or von Neumann bounded, if every neighborhood of the zero vector can be inflated to include the set. A set that is not bounded is called unbounded. Bounded sets are a natural way to define locally convex polar topologies on the vector spaces in a dual pair, as the polar set of a bounded set is an absolutely convex and absorbing set. The concept was first introduced by John von Neumann and Andrey Kolmogorov in 1935.

text:
# Bounded set (topological vector space)

In functional analysis and related areas of mathematics, a set in a topological vector space is called **bounded** or **von Neumann bounded**, if every neighborhood of the zero vector can be *inflated* to include the set. A set that is not bounded is called **unbounded**.

Bounded sets are a natural way to define locally convex polar topologies on the vector spaces in a dual pair, as the polar set of a bounded set is an absolutely convex and absorbing set. The concept was first introduced by John von Neumann and Andrey Kolmogorov in 1935.

## Definition

Suppose $X$ is a topological vector space (TVS) over a field $\mathbb {K} .$

A subset $B$ of $X$ is called ***von Neumann bounded*** or just ***bounded*** in $X$ if any of the following equivalent conditions are satisfied:

1. *Definition*: For every neighborhood $V$ of the origin there exists a real $r\>0$ such that $B\subseteq sV$ for all scalars $s$ satisfying $|s|\geq r.$
2. $B$ is absorbed by every neighborhood of the origin.
3. For every neighborhood $V$ of the origin there exists a scalar $s$ such that $B\subseteq sV.$
4. For every neighborhood $V$ of the origin there exists a real $r\>0$ such that $sB\subseteq V$ for all scalars $s$ satisfying $|s|\leq r.$
5. For every neighborhood $V$ of the origin there exists a real $r\>0$ such that $tB\subseteq V$ for all real $0\<t\leq r.$
6. Any one of statements (1) through (5) above but with the word "neighborhood" replaced by any of the following: "balanced neighborhood," "open balanced neighborhood," "closed balanced neighborhood," "open neighborhood," "closed neighborhood".
    * e.g. Statement (2) may become: $B$ is bounded if and only if $B$ is absorbed by every balanced neighborhood of the origin.
    * If $X$ is locally convex then the adjective "convex" may be also be added to any of these 5 replacements.
7. For every sequence of scalars $s\_{1},s\_{2},s\_{3},\ldots $ that converges to $0$ and every sequence $b\_{1},b\_{2},b\_{3},\ldots $ in $B,$ the sequence $s\_{1}b\_{1},s\_{2}b\_{2},s\_{3}b\_{3},\ldots $ converges to $0$ in $X.$
    * This was the definition of "bounded" that Andrey Kolmogorov used in 1934, which is the same as the definition introduced by Stanisław Mazur and Władysław Orlicz in 1933 for metrizable TVS. Kolmogorov used this definition to prove that a TVS is seminormable if and only if it has a bounded convex neighborhood of the origin.
8. For every sequence $b\_{1},b\_{2},b\_{3},\ldots $ in $B,$ the sequence $\textstyle \left({\tfrac {1}{i}b\_{i}\right)\_{i=1}^{\infty }}$ converges to $0$ in $X.$
9. Every countable subset of $B$ is bounded (according to any defining condition other than this one).

If $\mathcal {B}$ is a neighborhood basis for $X$ at the origin then this list may be extended to include:

10. Any one of statements (1) through (5) above but with the neighborhoods limited to those belonging to $\mathcal {B}.$
    * e.g. Statement (3) may become: For every $V\in {\mathcal {B}}$ there exists a scalar $s$ such that $B\subseteq sV.$

If $X$ is a locally convex space whose topology is defined by a family $\mathcal {P}$ of continuous seminorms, then this list may be extended to include:

11. $p(B)$ is bounded for all $p\in {\mathcal {P}.}$
12. There exists a sequence of non-zero scalars $s\_{1},s\_{2},s\_{3},\ldots $ such that for every sequence $b\_{1},b\_{2},b\_{3},\ldots $ in $B,$ the sequence $b\_{1}s\_{1},b\_{2}s\_{2},b\_{3}s\_{3},\ldots $ is bounded in $X$ (according to any defining condition other than this one).
13. For all $p\in {\mathcal {P},}$ $B$ is bounded (according to any defining condition other than this one) in the semi normed space $(X,p).$
14. B is weakly bounded, i.e. every continuous linear functional is bounded on B

If $X$ is a normed space with norm $\\|\cdot \\|$ (or more generally, if it is a seminormed space and $\\|\cdot \\|$ is merely a seminorm), then this list may be extended to include:

14. $B$ is a *norm bounded* subset of $(X,\\|\cdot \\|).$ By definition, this means that there exists a real number $r\>0$ such that $\\|b\\|\leq r$ for all $b\in B.$
15. $\sup \_{b\in B}\\|b\\|\<\infty .$
    * Thus, if $L:(X,\\|\cdot \\|)\to (Y,\\|\cdot \\|)$ is a linear map between two normed (or seminormed) spaces and if $B$ is the closed (alternatively, open) unit ball in $(X,\\|\cdot \\|)$ centered at the origin, then $L$ is a bounded linear operator (which recall means that its operator norm $\\|L\\|:=\sup \_{b\in B}\\|L(b)\\|\<\infty $ is finite) if and only if the image $L(B)$ of this ball under $L$ is a norm bounded subset of $(Y,\\|\cdot \\|).$
16. $B$ is a subset of some (open or closed) ball.
    * This ball need not be centered at the origin, but its radius must (as usual) be positive and finite.

If $B$ is a vector subspace of the TVS $X$ then this list may be extended to include:

17. $B$ is contained in the closure of $\\{0\\}.$
    * In other words, a vector subspace of $X$ is bounded if and only if it is a subset of (the vector space) $\operatorname {cl} \_{X}\\{0\\}.$
    * Recall that $X$ is a Hausdorff space if and only if $\\{0\\}$ is closed in $X.$ So the only bounded vector subspace of a Hausdorff TVS is $\\{0\\}.$

A subset that is not bounded is called *unbounded*.

### Bornology and fundamental systems of bounded sets

The collection of all bounded sets on a topological vector space $X$ is called the *von Neumann bornology* or the (*canonical*) *bornology of $X.$*

A *base* or *fundamental system of bounded sets* of $X$ is a set $\mathcal {B}$ of bounded subsets of $X$ such that every bounded subset of $X$ is a subset of some $B\in {\mathcal {B}.}$ The set of all bounded subsets of $X$ trivially forms a fundamental system of bounded sets of $X.$

#### Examples

In any locally convex TVS, the set of closed and bounded disks are a base of bounded set.

## Examples and sufficient conditions

Unless indicated otherwise, a topological vector space (TVS) need not be Hausdorff nor locally convex.

* Finite sets are bounded.
* Every totally bounded subset of a TVS is bounded.
* Every relatively compact set in a topological vector space is bounded. If the space is equipped with the weak topology the converse is also true.
* The set of points of a Cauchy sequence is bounded, the set of points of a Cauchy net need not be bounded.
* The closure of the origin (referring to the closure of the set $\\{0\\}$) is always a bounded closed vector subspace. This set $\operatorname {cl} \_{X}\\{0\\}$ is the unique largest (with respect to set inclusion $\\,\subseteq \\,$) bounded vector subspace of $X.$ In particular, if $B\subseteq X$ is a bounded subset of $X$ then so is $B+\operatorname {cl} \_{X}\\{0\\}.$

**Unbounded sets**

A set that is not bounded is said to be *unbounded*.

Any vector subspace of a TVS that is not a contained in the closure of $\\{0\\}$ is unbounded

There exists a Fréchet space $X$ having a bounded subset $B$ and also a dense vector subspace $M$ such that $B$ is *not* contained in the closure (in $X$) of any bounded subset of $M.$

### Stability properties

* In any TVS, finite unions, finite Minkowski sums, scalar multiples, translations, subsets, closures, interiors, and balanced hulls of bounded sets are again bounded.
* In any locally convex TVS, the convex hull (also called the convex envelope) of a bounded set is again bounded. However, this may be false if the space is not locally convex, as the (non-locally convex) Lp space $L^{p}$ spaces for $0\<p\<1$ have no nontrivial open convex subsets.
* The image of a bounded set under a continuous linear map is a bounded subset of the codomain.
* A subset of an arbitrary (Cartesian) product of TVSs is bounded if and only if its image under every coordinate projections is bounded.
* If $S\subseteq X\subseteq Y$ and $X$ is a topological vector subspace of $Y,$ then $S$ is bounded in $X$ if and only if $S$ is bounded in $Y.$
    + In other words, a subset $S\subseteq X$ is bounded in $X$ if and only if it is bounded in every (or equivalently, in some) topological vector superspace of $X.$

## Properties

A locally convex topological vector space has a bounded neighborhood of zero if and only if its topology can be defined by a *single* seminorm.

The polar of a bounded set is an absolutely convex and absorbing set.

**Mackey's countability condition**  If $B\_{1},B\_{2},B\_{3},\ldots $ is a countable sequence of bounded subsets of a metrizable locally convex topological vector space $X,$ then there exists a bounded subset $B$ of $X$ and a sequence $r\_{1},r\_{2},r\_{3},\ldots $ of positive real numbers such that $B\_{i}\subseteq r\_{i}B$ for all $i\in \mathbb {N} $ (or equivalently, such that $\tfrac {1}{r\_{1}B\_{1}\cup {\tfrac {1}{r\_{2}B\_{2}\cup {\tfrac {1}{r\_{3}B\_{3}\cup \cdots \subseteq B}}}}}$).

Using the definition of uniformly bounded sets given below, Mackey's countability condition can be restated as: If $B\_{1},B\_{2},B\_{3},\ldots $ are bounded subsets of a metrizable locally convex space then there exists a sequence $t\_{1},t\_{2},t\_{3},\ldots $ of positive real numbers such that $t\_{1}B\_{1},\\,t\_{2}B\_{2},\\,t\_{3}B\_{3},\ldots $ are uniformly bounded. In words, given any countable family of bounded sets in a metrizable locally convex space, it is possible to scale each set by its own positive real so that they become uniformly bounded.

## Generalizations

### Uniformly bounded sets

A family of sets $\mathcal {B}$ of subsets of a topological vector space $Y$ is said to be *uniformly bounded* in $Y,$ if there exists some bounded subset $D$ of $Y$ such that $B\subseteq D\quad {\text{ for every }B\in {\mathcal {B},}}$ which happens if and only if its union $\cup {\mathcal {B}~:=~\bigcup \_{B\in {\mathcal {B}B}}}$ is a bounded subset of $Y.$ In the case of a normed (or seminormed) space, a family $\mathcal {B}$ is uniformly bounded if and only if its union $\cup {\mathcal {B}}$ is *norm bounded*, meaning that there exists some real $M\geq 0$ such that $\textstyle \\|b\\|\leq M$ for every $b\in \cup {\mathcal {B},}$ or equivalently, if and only if $\textstyle \sup \_{\stackrel {b\in B}{B\in {\mathcal {B}\\|b\\|\<\infty .}}}$

A set $H$ of maps from $X$ to $Y$ is said to be *uniformly bounded on a given set* $C\subseteq X$ if the family $H(C):=\\{h(C):h\in H\\}$ is uniformly bounded in $Y,$ which by definition means that there exists some bounded subset $D$ of $Y$ such that $h(C)\subseteq D{\text{ for all }h\in H,}$ or equivalently, if and only if $\textstyle \cup H(C):=\bigcup \_{h\in H}h(C)$ is a bounded subset of $Y.$ A set $H$ of linear maps between two normed (or seminormed) spaces $X$ and $Y$ is uniformly bounded on some (or equivalently, every) open ball (and/or non-degenerate closed ball) in $X$ if and only if their operator norms are uniformly bounded; that is, if and only if $\textstyle \sup \_{h\in H}\\|h\\|\<\infty .$

**Proposition**  Let $H\subseteq L(X,Y)$ be a set of continuous linear operators between two topological vector spaces $X$ and $Y$ and let $C\subseteq X$ be any bounded subset of $X.$ Then $H$ is uniformly bounded on $C$ (that is, the family $\\{h(C):h\in H\\}$ is uniformly bounded in $Y$) if any of the following conditions are satisfied:

1. $H$ is equicontinuous.
2. $C$ is a convex compact Hausdorff subspace of $X$ and for every $c\in C,$ the orbit $H(c):=\\{h(c):h\in H\\}$ is a bounded subset of $Y.$

| Proof of part (1) |
| --- |
| Assume $H$ is equicontinuous and let $W$ be a neighborhood of the origin in $Y.$ Since $H$ is equicontinuous, there exists a neighborhood $U$ of the origin in $X$ such that $h(U)\subseteq W$ for every $h\in H.$ Because $C$ is bounded in $X,$ there exists some real $r\>0$ such that if $t\geq r$ then $C\subseteq tU.$ So for every $h\in H$ and every $t\geq r,$ $h(C)\subseteq h(tU)=th(U)\subseteq tW,$ which implies that $\textstyle \bigcup \_{h\in H}h(C)\subseteq tW.$ Thus $\textstyle \bigcup \_{h\in H}h(C)$ is bounded in $Y.$ Q.E.D. |

| Proof of part (2) |
| --- |
| Let $W$ be a balanced neighborhood of the origin in $Y$ and let $V$ be a closed balanced neighborhood of the origin in $Y$ such that $V+V\subseteq W.$ Define $E~:=~\bigcap \_{h\in H}h^{-1}(V),$ which is a closed subset of $X$ (since $V$ is closed while every $h:X\to Y$ is continuous) that satisfies $h(E)\subseteq V$ for every $h\in H.$ Note that for every non-zero scalar $n\neq 0,$ the set $nE$ is closed in $X$ (since scalar multiplication by $n\neq 0$ is a homeomorphism) and so every $C\cap nE$ is closed in $C.$
It will now be shown that $C\subseteq \bigcup \_{n\in \mathbb {N} }nE,$ from which $C=\bigcup \_{n\in \mathbb {N} }(C\cap nE)$ follows. If $c\in C$ then $H(c)$ being bounded guarantees the existence of some positive integer $n=n\_{c}\in \mathbb {N} $ such that $H(c)\subseteq n\_{c}V,$ where the linearity of every $h\in H$ now implies $\tfrac {1}{n\_{c}c\in h^{-1}(V);}$ thus $\tfrac {1}{n\_{c}c\in \bigcap \_{h\in H}h^{-1}(V)=E}$ and hence $C\subseteq \bigcup \_{n\in \mathbb {N} }nE,$ as desired.
Thus $\textstyle C=(C\cap 1E)\cup (C\cap 2E)\cup (C\cap 3E)\cup \cdots $ expresses $C$ as a countable union of closed (in $C$) sets. Since $C$ is a nonmeager subset of itself (as it is a Baire space by the Baire category theorem), this is only possible if there is some integer $n\in \mathbb {N} $ such that $C\cap nE$ has non-empty interior in $C.$ Let $k\in \operatorname {Int} \_{C}(C\cap nE)$ be any point belonging to this open subset of $C.$ Let $U$ be any balanced open neighborhood of the origin in $X$ such that $C\cap (k+U)~\subseteq ~\operatorname {Int} \_{C}(C\cap nE).$
The sets $\\{k+pU:p\>1\\}$ form an increasing (meaning $p\leq q$ implies $k+pU\subseteq k+qU$) cover of the compact space $C,$ so there exists some $p\>1$ such that $C\subseteq k+pU$ (and thus $\tfrac {1}{p}(C-k)\subseteq U$). It will be shown that $h(C)\subseteq pnW$ for every $h\in H,$ thus demonstrating that $\\{h(C):h\in H\\}$ is uniformly bounded in $Y$ and completing the proof. So fix $h\in H$ and $c\in C.$ Let $z~:=~{\tfrac {p-1}{p}k+{\tfrac {1}{p}c.}}$
The convexity of $C$ guarantees $z\in C$ and moreover, $z\in k+U$ since $z-k={\tfrac {-1}{p}k+{\tfrac {1}{p}c={\tfrac {1}{p}(c-k)\in {\tfrac {1}{p}(C-k)\subseteq U.}}}}$ Thus $z\in C\cap (k+U),$ which is a subset of $\operatorname {Int} \_{C}(C\cap nE).$ Since $nV$ is balanced and $|1-p|=p-1\<p,$ we have $(1-p)nV\subseteq pnV,$ which combined with $h(E)\subseteq V$ gives $pnh(E)+(1-p)nh(E)~\subseteq ~pnV+(1-p)nV~\subseteq ~pnV+pnV~\subseteq ~pn(V+V)~\subseteq ~pnW.$ Finally, $c=pz+(1-p)k$ and $k,z\in nE$ imply $h(c)~=~ph(z)+(1-p)h(k)~\in ~pnh(E)+(1-p)nh(E)~\subseteq ~pnW,$ as desired. Q.E.D. |

Since every singleton subset of $X$ is also a bounded subset, it follows that if $H\subseteq L(X,Y)$ is an equicontinuous set of continuous linear operators between two topological vector spaces $X$ and $Y$ (not necessarily Hausdorff or locally convex), then the orbit $\textstyle H(x):=\\{h(x):h\in H\\}$ of every $x\in X$ is a bounded subset of $Y.$

### Bounded subsets of topological modules

The definition of bounded sets can be generalized to topological modules. A subset $A$ of a topological module $M$ over a topological ring $R$ is bounded if for any neighborhood $N$ of $0\_{M}$ there exists a neighborhood $w$ of $0\_{R}$ such that $wA\subseteq B.$

**Notes**

1. For any set $A$ and scalar $s,$ the notation $sA$ denotes the set $sA:=\\{sa:a\in A\\}.$
2. This means that the topology on $X$ is equal to the topology induced on it by $\\|\cdot \\|.$ Note that every normed space is a seminormed space and every norm is a seminorm. The definition of the topology induced by a seminorm is identical to the definition of the topology induced by a norm.
3. If $(X,\\|\cdot \\|)$ is a normed space or a seminormed space, then the open and closed balls of radius $r\>0$ (where $r\neq \infty $ is a real number) centered at a point $x\in X$ are, respectively, the sets $\textstyle B\_{\<r}(x):=\\{z\in X:\\|z-x\\|\<r\\}$ and $\textstyle B\_{\leq r}(x):=\\{z\in X:\\|z-x\\|\leq r\\}.$ Any such set is called a (non-degenerate) *ball*.

## Bibliography


title: Pierre-Henri Philibert

abstract: Pierre-Henri Philibert was a French Navy officer.

text:
# Pierre-Henri Philibert

**Pierre-Henri Philibert** (24 January 1774 in Saint-Denis, Île Bourbon – 31 October 1824 in Paris) was a French Navy officer.

## Career

Philibert was born the family of a Navy civil servant. He joined the Navy in 1786.

During the French Revolution, on 16 November 1793, Philibert was promoted to Ensign. He rose to Lieutenant in 1803, and served as aid to Rear-Admiral Magon on the 74-gun *Algésiras*. He took part in the Battle of Trafalgar, distinguishing himself by recapturing *Algésiras* after the battle and sailing her back to Cádiz.

By June 1809, Philibert was in command of *Sapho*, on which he voyaged to India. *Sapho* sailed from Bordeaux to Port-des-Barques between around 1 July. Philibert was promoted to Commander in 1811, after 26 April.

From 7 October 1813, Philibert led a frigate division, comprising *Étoile* and *Sultane*, under Abel Aubert du Petit-Thouars, to engage in commerce raiding. Philibert commanded the French forces at the Battle of Jobourg, where both frigates of his squadron were captured.

Philibert was promoted to Captain (second class) in 1814. By 1815, Philibert was a Knight in the Legion of Honour and the Order of Saint Louis.

At the end of the Hundred Days, Philibert was in command of the frigate *Saale* and led a squadron comprising her and *Méduse*, under Captain Ponée. A historic rumour has it that with Napoléon's armies in disarray, Ponée proposed to have ferry Napoléon to America on *Saale*, while *Méduse* would have engaged HMS *Bellerophon* in a hopeless battle to prevent her from giving chase. Whether the plan was indeed ever formulated or not, it was never implemented, and Napoléon instead abdicated for the second time. From 14 April 1815 to 15 December, he conducted a mission to India on his frigate, by then renamed to *Amphitrite*. In 1816, he was in command of a full division, comprising the fluyts *Licorne*, under Lieutenant and later Commander Rouvroy de Saint-Simon, and *Éléphant*, under Commander de Cheffontaines, in addition to *Amphitrite*. By 1817, the Division further comprised the frigate *Cybèle*, under Captain Achille de Kergariou; the storeships *Alouette*, under Lieutenant Rigodit, and *Girouette*, under Ensign Lemaarant de Kerdaniel; and the merchantman *Célestine* and *Louise*. In 1818, the Division comprised *Cybèle*, the fluyts *Normande* and *Rhône* and the storeship *Durance*.

In 1820, Philibert commander the Expédition d'Asie, with his flag on *Rhône* and later on *Durance*. His voyages are credited for bringing vanilla to La Réunion, creating the Bourbon vanilla cultivar.

He was promoted to Officer on the Legion of Honour in 1821, and Captain (1st class) in 1822.

## Notes and references

### Notes

### References

1. Naissance de la Vanille Bourbon, Histoire de la vanille
2. Acte naissance Anom St Denis Réunion 1774 (p. 2-3/26)
3. Note 246 of the *Mémoires du Baron de Bonnefoux, Capitaine de Vaisseau, 1782–1855*
4. *Fonds Marine*, p. 338
5. *Fonds Marine*, p. 387
6. Roche, p. 405
7. *Fonds Marine*, p. 444
8. *The Royal Navy: A History from the Earliest Times to the Present*, vol.5
9. *Fonds Marine*, Vol. 2, p. 494.
10. Guérin, p. 482
11. *Fonds Marine*, Vol. 2, p. 502.
12. *Fonds Marine*, Vol. 2, p. 507.
13. *Fonds Marine*, Vol. 2, p. 514-515.
14. *Fonds Marine*, Vol. 2, p. 539.

### Bibliography

* "Fonds Marine. Campagnes (opérations ; divisions et stations navales ; missions diverses). Inventaire de la sous-série Marine BB4. Tome deuxième : BB4 1 à 482 (1790-1826)" (PDF). *servicehistorique.sga.defense.gouv.fr*. Service historique du Ministère de la Défense. Archived from the original (PDF) on 29 September 2015. Retrieved 6 May 2013.
* Guérin, Léon (1857). *Histoire maritime de France* (in French). Vol. 6. Dufour et Mulat.
* Roche, Jean-Michel (2005). *Dictionnaire des bâtiments de la flotte de guerre française de Colbert à nos jours*. Vol. 1. Group Retozel-Maury Millau. p. 169. ISBN 978-2-9525917-0-6. OCLC 165892922.

## InfoBox

| Pierre-Henri Philibert | |
| --- | --- |
| Pierre-Henri Philibert | |
| Born | (1774-01-24)24 January 1774
Saint-Denis, La Réunion |
| Died | (1824-10-31)31 October 1824
Paris |
| Allegiance | France |
| Service/branch | French Navy |
| Rank | Captain |