Topologically complete representations of inverse semigroups
type: Item
instance of: scholarly article
title: Topologically complete representations of inverse semigroups
zbMATH Open document ID: 1016.20049
author: Grigori I. Zhitomirski
published in: Semigroup Forum
publication date: 2003-03-18T00:00:00Z
review text: A representation of an inverse semigroup by means of partial open homeomorphisms of a topological \(T_0\)-space \(X\) is called topologically complete if the domains of these partial homeomophisms form a base of the topology of \(X\). The author gives a method for constructing topologically complete representations by means of special ternary relations. This method makes it possible to obtain a pseudo-elementary axiomatization in \(T_1\), \(T_2\), and \(T_3\)-spaces. Also, the author proves that any antigroup has a natural topological structure \(\tau\) such that all of its faithful topologically complete representations are continuous, and \(\tau\) is the minimal topology with this property.
Mathematics Subject Classification ID: 20M30
Mathematics Subject Classification ID: 20M18
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 54H10
Mathematics Subject Classification ID: 54H15
Mathematics Subject Classification ID: 22A15
zbMATH DE Number: 1883944
zbMATH Keywords: topologically complete representations
zbMATH Keywords: inverse semigroups
zbMATH Keywords: partial open homeomorphisms
zbMATH Keywords: ternary relations
zbMATH Keywords: pseudo-elementary axiomatizations
zbMATH Keywords: antigroups
zbMATH Keywords: minimal topologies
reviewed by: O. Gutik
MaRDI profile type: Publication
full work available at URL: s002330010153
OpenAlex ID: W2004100976
DOI: 10.1007/S002330010153
description: scientific article; zbMATH DE number 1883944