On hereditarily normal compact spaces, in which regular closed subsets are \(G_ \delta\)-sets
type: Item
instance of: scholarly article
title: On hereditarily normal compact spaces, in which regular closed subsets are \(G_ \delta\)-sets
zbMATH Open document ID: 0812.54006
DOI: 10.1016/0166-8641(94)90128-7
author: D. P. Baturov
published in: Topology and its Applications
publication date: 1994-09-20T00:00:00Z
review text: A topological space \(X\) is \(k\)-perfect if every regular closed subset of \(X\) is a \(G_ \delta\)-set. Some properties of hereditarily normal \(k\)- perfect spaces are considered. Let \({\mathcal K}\) denote the class of all hereditarily normal \(k\)-perfect compact spaces. Every \(X \in {\mathcal K}\) has countable tightness and, under \(2^ \omega = \omega_ 2\), countable spread. The assertion ``every \(X\) in \({\mathcal K}\) is perfectly normal'' is independent of and consistent with ZFC: under \(\diamondsuit\) there exists a space \(X\) in \({\mathcal K}\) which is not perfectly normal (Theorem 2.3), while under \(MA + 2^ \omega = \omega_ 2\) every \(X \in {\mathcal K}\) is perfectly normal (Theorem 3.6).
Mathematics Subject Classification ID: 54A35
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54D30
Mathematics Subject Classification ID: 54G20
zbMATH DE Number: 612395
zbMATH Keywords: \(k\)-perfect spaces
zbMATH Keywords: hereditarily normal \(k\)-perfect compact spaces
zbMATH Keywords: tightness
zbMATH Keywords: spread
reviewed by: Ljubiša D. R. Kočinac
MaRDI profile type: Publication
full work available at URL: 0166-8641(94)90128-7
OpenAlex ID: W2021851203
cites work: Q4150804
cites work: Q3938195
cites work: Calibers, free sequences and density
cites work: On Countably Compact, Perfectly Normal Spaces
cites work: Q3914038
description: scientific article; zbMATH DE number 612395