Locally compact, countably paracompact spaces in the constructible universe (Q1113126)

The author's summary: ``It is proved that under V\(=L\), every locally compact, countably paracompact space is collectionwise normal with respect to compact sets. From this it can be shown that under \(V=L\), submetacompact implies paracompact in the class of locally compact, countably paracompact spaces.'' The author then shows that \(V=L\) cannot be omitted. ``Indeed, under MA\(+\neg CH\), the Cantor tree constructed from a Q-set is an example of a countably paracompact, locally compact space which is not even collectionwise Hausdorff [see \textit{F. Tall}, Handbook of set-theoretic topology, 685-732 (1984; Zbl 0552.54011)].'' He also notes that collectionwise normal with respect to compact sets cannot be replaced with collectionwise normal [see \textit{P. Daniels} and \textit{G. Gruenhage}, Proc. Am. Math. Soc. 95, 115-118 (1985; Zbl 0586.54029)].