Normality and collectionwise normality of product spaces. II
type: Item
instance of: scholarly article
title: Normality and collectionwise normality of product spaces. II
zbMATH Open document ID: 0927.54006
author: Kaori Yamazaki
published in: Tsukuba Journal of Mathematics
publication date: 1999-12-13T00:00:00Z
review text: For Part I see [Topol. Proc. 22, 383-392 (1997; Zbl 0918.54027) ]. As for the product space \(X\times Y\), the author proves the equivalence of its normality and its collectionwise normality in the following cases which are generalizations of known results. (i) \(X\) is a collectionwise normal \(\Sigma\)-space and \(Y\) is a collectionwise normal first countable \(P\)-space. (ii) \(X\) is the closed, continuous image of a normal \(M\)-space and \(Y\) is a collectionwise normal first countable \(P\)-space. (iii) \(X\) is the closed, continuous image of a paracompact \(M\)-space and \(Y\) is a collectionwise normal \(P\)-space. It is also proved that in case (iii), if \(Y\) is a paracompact \(P\)-space, then \(X\times Y\) is paracompact if and only if \(X\times Y\) is normal. All spaces are assumed at least being Hausdorff.
reviewed by: Akihiro Okuyama
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 54D15
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 54E18
zbMATH DE Number: 1309333
zbMATH Keywords: \(P\)-space
zbMATH Keywords: \(M\)-space
zbMATH Keywords: collectionwise normality
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496163679
OpenAlex ID: W562271113
DOI: 10.21099/TKBJM/1496163679
description: scientific article; zbMATH DE number 1309333