Cellularity in subgroups of paratopological groups
type: Item
instance of: scholarly article
title: Cellularity in subgroups of paratopological groups
zbMATH Open document ID: 1321.22007
author: Artur Hideyuki Tomita
author: Mikhail Tkachenko
published in: Topology and its Applications
publication date: 2015-08-19T00:00:00Z
review text: A paratopological (semitopological) group is a group with a topology such that multiplication on the group is jointly (separately) continuous. In this paper, it is proved that every subgroup of a \(\sigma\)-compact \(T_1\) paratopological group has countable cellularity (but this conclusion fails for subgroups of \(\sigma\)-compact \(T_0\) paratopological groups) and that if \(S\) is a non-empty subsemigroup of a topologically periodic semitopological group \(G\), then the closure of \(S\) is a subgroup of \(G\). This implies, in particular, that the closure of every non-empty subsemigroup of a precompact topological group \(G\) is a subgroup of \(G\) and that every subsemigroup of \(G\) has countable cellularity.
Mathematics Subject Classification ID: 22A30
Mathematics Subject Classification ID: 54H11
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54G20
zbMATH DE Number: 6473614
zbMATH Keywords: cellularity
zbMATH Keywords: \(\sigma\)-compact
zbMATH Keywords: subsemigroup
zbMATH Keywords: precompact
zbMATH Keywords: topologically periodic
reviewed by: Yuri Movsisyan
MaRDI profile type: Publication
full work available at URL: j.topol.2015.05.081
OpenAlex ID: W904203432
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DOI: 10.1016/J.TOPOL.2015.05.081
description: scientific article; zbMATH DE number 6473614