Three examples of pseudocompact quasitopological groups
type: Item
instance of: scholarly article
title: Three examples of pseudocompact quasitopological groups
zbMATH Open document ID: 1113.54023
published in: Topology and its Applications
publication date: 2007-01-09T00:00:00Z
review text: It is known that the product of an arbitrary family of pseudocompact topological groups is pseudocompact and both a topological group of countable cellularity and a pseudocompact topological group are Moscow spaces, where a space \(X\) is called \textit{Moscow} if the closure of every open subset of \(X\) is the union of a family of \(G_{\delta}\)-sets in \(X\). In this paper, the authors show that the above results for topological groups cannot be extended to quasitopological groups. Indeed, they show that there exist two pseudocompact quasitopological groups whose product is not pseudocompact and a pseudocompact quasitopological group of countable cellularity such that it is not Moscow.
reviewed by: Kohzo Yamada
Mathematics Subject Classification ID: 54H13
Mathematics Subject Classification ID: 22A15
Mathematics Subject Classification ID: 54G20
Mathematics Subject Classification ID: 54A25
zbMATH DE Number: 5083225
zbMATH Keywords: quasitopological group
zbMATH Keywords: pseudocompact space
zbMATH Keywords: Moscow space
zbMATH Keywords: cellularity
zbMATH Keywords: discrete subgroup
author: C. Hernández
author: Mikhail Tkachenko
MaRDI profile type: Publication
full work available at URL: j.topol.2006.03.023
OpenAlex ID: W2005338571
cites work: Q4424979
cites work: Q4828840
cites work: On the product of homogeneous spaces
cites work: Pseudocompactness and uniform continuity in topological groups
cites work: The Product of Two Countably Compact Topological Groups
cites work: Q4150804
cites work: Q4021986
cites work: Q3957613
DOI: 10.1016/J.TOPOL.2006.03.023
description: scientific article; zbMATH DE number 5083225