The D-property of monotone covering properties and related conclusions
type: Item
instance of: scholarly article
title: The D-property of monotone covering properties and related conclusions
zbMATH Open document ID: 1252.54017
author: Liang-Xue Peng
author: Hui Li
published in: Topology and its Applications
publication date: 2012-09-19T00:00:00Z
review text: In this note, it is shown that every monotonically (countably) metacompact space is hereditarily a \(D\)-space and every monotonically meta-Lindelöf space is hereditarily dually \(\sigma\)-closed discrete. As a corollary, it is shown that if \(X\) is a monotonically meta-Lindelöf (or monotonically (countably) metacompact) monotonically normal space then \(X\) is hereditarily paracompact. In the second part of this note, the authors show that every scattered partition of a hereditarily almost thickly covered space is almost thick, and hence a hereditarily almost thickly covered space is \(aD\) and linearly \(D\). This answers a question of Guo and Junnila. It is also shown that every monotonically \(\omega\)-monolithic compact space is monotonically monolithic. This answers a question of Alas, Tkachuk and Wilson.
reviewed by: Maximilian Ganster
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 54E30
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 6084114
zbMATH Keywords: \(D\)-space
zbMATH Keywords: monotonically countably metacompact
zbMATH Keywords: monotonically meta-Lindelöf
zbMATH Keywords: almost thick cover
zbMATH Keywords: monotonically \(\omega\)-monolithic
MaRDI profile type: Publication
full work available at URL: j.topol.2012.07.009
OpenAlex ID: W2078460035
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DOI: 10.1016/J.TOPOL.2012.07.009
description: scientific article; zbMATH DE number 6084114