An algebraic version of Tamano's theorem for countably compact spaces
type: Item
instance of: scholarly article
title: An algebraic version of Tamano's theorem for countably compact spaces
zbMATH Open document ID: 1198.54054
author: Raushan Z. Buzyakova
published in: Topology and its Applications
publication date: 2010-08-27T00:00:00Z
review text: The author shows that if a space \(X\) is countably compact but not compact then one can find a compact space \(K\) such that \(X + K\) does not embed closedly into any normal topological group. Additionally she proves that for a countably compact space \(X\), which is not compact, no normal topological group contains a closed copy of \(X + (\tau\;+ 1)\), where \(\tau\) is the successor cardinal of \(\beta\,\, X \) and \(\beta\,\, X\) denotes the Stone-Čech compactification of \(X\). At last it is proved that if the cross-product of a space X is countably compact and normal and X not compact then no normal topological group contains a closed copy of \(X\) + \(bX\), where \(bX\) is an arbitrary Hausdorff compactification of \(X\).
reviewed by: Dieter Leseberg
Mathematics Subject Classification ID: 54D30
Mathematics Subject Classification ID: 54H11
Mathematics Subject Classification ID: 22C05
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 54D35
zbMATH DE Number: 5775744
zbMATH Keywords: topological group
zbMATH Keywords: countably compact space
zbMATH Keywords: ordinal
zbMATH Keywords: normal topological group
zbMATH Keywords: topological product space
MaRDI profile type: Publication
full work available at URL: j.topol.2010.06.008
OpenAlex ID: W1993191753
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DOI: 10.1016/J.TOPOL.2010.06.008
description: scientific article; zbMATH DE number 5775744