re paracompact.

The extra ingredient is that the local connectedness will enable us to decompose the space into a sum of pieces with Lindelöf number $\leq\aleph_1$. More precisely,

A space $X$ is of **Type I** if $X=\bigcup\{X_\alpha:\alpha\in\omega_1\}$, where each $X_\alpha$ is open, $\alpha<\beta$ implies $\overline{X}_\alpha\subseteq X_\beta$, and each $X_\alpha$ is Lindelöf.

In [@T], it is shown on page 104 that, assuming ${\mathbf{\mathop{\pmb{\sum}}}}$ and hereditary $\aleph_1$-collectionwise Hausdorffness for a locally compact hereditarily normal space not including a perfect pre-image of $\omega_1$ that the closure of a Lindelöf subspace is Lindelöf. Then we quote:

If $X$ is locally compact, locally connected, and countably tight, then $X$ is a topological sum of Type I spaces if and only if every Lindelöf subspace of $X$ has Lindelöf closure.

Since a topological sum of paracompact spaces is paracompact, this will complete the proof of the Theorem.

It may be of interest that **SRP** implies a weaker version of the conclusion of Theorem \[thm35\].2.

implies every first countable, monotonically normal space satisfying the MOP is paracompact.

Suppose $S$ is a first countable stationary subspace of some regular cardinal. Then each $s\in S$ is an $\omega$-cofinal ordinal.

Each $s\in S$ is either isolated in $S$ or is a limit of some subset of $S$. By first countability, in the latter case, each such $s$ is a limit of a sequence of elements of $S$.

Suppose not. Then by [@BR] the space includes a copy of a stationary subset of some regular cardinal. By [@J 37.18] **SRP** implies that that stationary set includes a copy of a closed unbounded subset of $\omega_1$. That copy is closed, countably compact but not compact, contradicting the MOP.

We conjecture th answer is positive. Large cardinals would be necessary to refute the existence of such a space, since an example can be constructed from the failure of the Covering Lemma for the Core Model K, which entails the consistency of measurable cardi