Bicompleting the left quasi-uniformity of a paratopological group
type: Item
instance of: scholarly article
title: Bicompleting the left quasi-uniformity of a paratopological group
zbMATH Open document ID: 0898.54024
author: Salvador Romaguera
author: Josefa Marín
published in: Archiv der Mathematik
publication date: 1998-11-01T00:00:00Z
review text: Extending results from the theory of topological groups to paratopological groups, the authors show that the bicompletion of the left quasi-uniformity of a paratopological \((T_0)\)-group \(G\) can be considered a topological semigroup which contains \(G\) as a sup-dense subsemigroup. Furthermore they characterize those paratopological \((T_0)\)-groups \(G\) for which the bicompletion of the left quasi-uniformity is a group \(H\) by the condition that each filter which is Cauchy with respect to the left uniformity is also Cauchy with respect to the right uniformity of the topological group associated with \(G\); under the latter condition the bicompleted left quasi-uniformity of \(G\) yields the left quasi-uniformity of the paratopological group \(H\). \{A paratopological group is a pair \((G,\tau)\) where \(G\) is a group and \(\tau\) is a topology on \(G\) such that the function \(\Psi: (G\times G,\tau\times \tau)\to (G,\tau)\) defined by \(\Psi(x,y)= xy\) is continuous\}.
Mathematics Subject Classification ID: 54E15
Mathematics Subject Classification ID: 22A05
Mathematics Subject Classification ID: 22A15
zbMATH DE Number: 1145389
zbMATH Keywords: right quasi-uniformity
zbMATH Keywords: bicompletion
zbMATH Keywords: left quasi-uniformity
zbMATH Keywords: paratopological group
reviewed by: Hans Peter Künzi
MaRDI profile type: Publication
full work available at URL: s000130050171
OpenAlex ID: W2070720300
DOI: 10.1007/S000130050171
description: scientific article; zbMATH DE number 1145389