Locally compact, countably paracompact spaces in the constructible universe
type: Item
instance of: scholarly article
title: Locally compact, countably paracompact spaces in the constructible universe
zbMATH Open document ID: 0661.54020
DOI: 10.1016/0166-8641(88)90077-6
published in: Topology and its Applications
publication date: 1988-01-01T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 54A35
Mathematics Subject Classification ID: 54D45
zbMATH DE Number: 4080373
zbMATH Keywords: V\(=L\)
zbMATH Keywords: locally compact, countably paracompact space
zbMATH Keywords: \(MA+\neg CH\)
zbMATH Keywords: Cantor tree
zbMATH Keywords: collectionwise Hausdorff
zbMATH Keywords: collectionwise normal
author: Z. Balogh
reviewed by: Charles E. Aull
MaRDI profile type: Publication
full work available at URL: 0166-8641(88)90077-6
OpenAlex ID: W2094579741
cites work: On collectionwise Hausdorffness in countably paracompact, locally compact spaces
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cites work: Separation in Countably Paracompact Spaces
description: scientific article; zbMATH DE number 4080373