Rajkov remainder and other group-remainders of a topological group
type: Item
instance of: scholarly article
title: Rajkov remainder and other group-remainders of a topological group
zbMATH Open document ID: 1401.54018
published in: Topology and its Applications
publication date: 2018-06-25T00:00:00Z
review text: The paper is a study of dense subgroups of topological groups and their remainders. Recall that \(X\) is a Lindelöf \(p\)-space, if there exists a perfect map \(f:X\to M\) of \(X\) onto a separable metrizable space \(M\). If separability of \(M\) is omitted in the above definition, then \(X\) is called a paracompact \(p\)-space. If \(G\) is a dense subgroup of a topological group \(B\), then \(X=B\setminus G\) is called a \(g\)-remainder of \(G\) and \(B\) is a group extension of \(G\). The authors establish that, for any topological group \(G\), if \(X\) is a Lindelöf \(g\)-remainder of \(G\) which contains a compact subspace of countable character in \(X\), then both \(G\) and \(X\) are Lindelöf \(p\)-spaces. Besides, any \(g\)-remainder of \(G\) is a Lindelöf \(p\)-space. It is also proved that if some non-empty \(g\)-remainder of \(G\) is a paracompact \(p\)-space, then \(G\) is itself a paracompact \(p\)-space.
Mathematics Subject Classification ID: 54H11
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54B05
Mathematics Subject Classification ID: 54D40
zbMATH DE Number: 6893994
zbMATH Keywords: topological group
zbMATH Keywords: group-extension
zbMATH Keywords: paracompact \(p\)-space
zbMATH Keywords: Lindelöf \(p\)-space
zbMATH Keywords: \(g\)-remainder
zbMATH Keywords: Rajkov remainder
author: A. V. Arhangel'skii
author: Mitrofan M. Choban
reviewed by: Vladimir Tkachuk
MaRDI profile type: Publication
full work available at URL: j.topol.2018.03.024
OpenAlex ID: W2794766999
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Wikidata QID: Q130111011
DOI: 10.1016/J.TOPOL.2018.03.024
description: scientific article; zbMATH DE number 6893994