Weakly normal topological spaces and products,
type: Item
instance of: scholarly article
title: Weakly normal topological spaces and products,
zbMATH Open document ID: 0874.54020
DOI: 10.1016/S0166-8641(96)00115-0
author: Andrew N. Yakivchik
published in: Topology and its Applications
publication date: 1997-10-28T00:00:00Z
review text: \textit{A. V. Arkhangel'skij} defined weakly normal spaces over a class \(\mathcal P\) of spaces in [Math. Res. 67, 13-26 (1992; Zbl 0792.54003)] and posed several problems concerning productivity of weak normality. Among others, the present paper shows that: (1) Weak normality is not closed under sums; (2) A Tikhonov space \(X\) is paracompact iff \(X\times cX\) is weakly normal over metric spaces for some compactification \(cX\); (3) The product of the Tikhonov plank with any first countable Hausdorff space is weakly normal; (4) If \(X\times cX\) is weakly normal for a pseudocompact Tikhonov space \(X\) and its compactification \(cX\), then \(X\) is realcompact (i.e., compact). Some results deal with hereditary weak normality.
reviewed by: M. Hušek
Mathematics Subject Classification ID: 54D15
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54A20
Mathematics Subject Classification ID: 54D35
zbMATH DE Number: 993991
zbMATH Keywords: weakly normal space
zbMATH Keywords: products
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 993991