Dense subgroups of paratopological groups
type: Item
instance of: scholarly article
title: Dense subgroups of paratopological groups
zbMATH Open document ID: 1329.54037
author: Iván Sánchez
published in: Topology and its Applications
publication date: 2015-11-16T00:00:00Z
review text: A paratopological group (semitopological group) is a group with a topology such that the multiplication operation is jointly (separately) continuous. In this paper, the author focus on some properties in semitopological groups which are preserved or determined by dense subgroups. Many propositions for this kind of properties are given. For example, (1) letting \(H\) be a dense subgroup of a \(T_3\) semitopological group \(G\), if \(H\) is a paratopological group, then \(G\) is a paratopological group as well; (2) a semitopological group \(G\) is a topological group iff \(G\) is \(T_3\) and it contains a dense topological subgroup. Many counterexamples for this kind of properties are also presented in this paper. In the end, the author answers a problem posed by \textit{M. Tkachenko} [Topology Appl. 179, 200--214 (2015; Zbl 1305.54024)] in the negative.
reviewed by: Longyun Ding
Mathematics Subject Classification ID: 54H11
Mathematics Subject Classification ID: 54D10
Mathematics Subject Classification ID: 54B30
Mathematics Subject Classification ID: 54C10
zbMATH DE Number: 6509447
zbMATH Keywords: semitopological group
zbMATH Keywords: paratopological group
zbMATH Keywords: dense subgroup
zbMATH Keywords: \(T_i\)-reflection
MaRDI profile type: Publication
full work available at URL: j.topol.2015.09.047
OpenAlex ID: W2176983436
cites work: Topological groups and related structures
cites work: Q3994935
cites work: Subgroups of paratopological groups and feebly compact groups
cites work: Q5185667
cites work: On H-closed paratopological groups
cites work: Paratopological groups. II
cites work: Cardinal invariants of paratopological groups
cites work: Paratopological groups with a \(G_\delta\)-diagonal of infinite rank
cites work: Axioms of separation in semitopological groups and related functors
cites work: Axioms of separation in paratopological groups and reflection functors
cites work: Group reflection and precompact paratopological groups
DOI: 10.1016/J.TOPOL.2015.09.047
description: scientific article; zbMATH DE number 6509447