Note on hereditary normality of product spaces
type: Item
instance of: scholarly article
title: Note on hereditary normality of product spaces
zbMATH Open document ID: 0902.54012
DOI: 10.1016/S0166-8641(97)00059-X
published in: Topology and its Applications
publication date: 1998-12-07T00:00:00Z
review text: Paracompact spaces \(X\) are constructed that are weak \(P(\omega)\) but not \(P(\omega)\), i.e., \(X\times Y\) is paracompact for every \(K\)-analytic space \(Y\), and not normal for some separable metrizable \(Y\). It is proved for a separable metrizable \(X\) that \(X\times Y\) is hereditarily normal for every hereditarily normal weak \(P(\omega)\)-space \(Y\) iff \(X\) is countable. In connection with the above results, the following problem is posed: In order that \(X\times Y\) be normal for any normal weak \(P(\omega)\)-space \(Y\), is it necessary that \(X\) be a \(K\)-analytic space?
reviewed by: M. Hušek
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 54D15
Mathematics Subject Classification ID: 54D20
zbMATH DE Number: 1121473
zbMATH Keywords: normality
zbMATH Keywords: paracompactness
zbMATH Keywords: product
author: Akihiro Okuyama
author: Stephen Watson
MaRDI profile type: Publication
cites work: Nonshrinking open covers and K. Morita's third conjecture
cites work: The product of a normal space and a metric space need not be normal
cites work: Products of normal spaces with metric spaces
cites work: Q5733140
cites work: Q4276156
full work available at URL: s0166-8641(97)00059-x
OpenAlex ID: W2013319867
description: scientific article; zbMATH DE number 1121473