On topological congruences of a topological semigroup
type: Item
instance of: scholarly article
title: On topological congruences of a topological semigroup
zbMATH Open document ID: 1244.22002
author: Behnam Khosravi
published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series
publication date: 2012-05-03T00:00:00Z
full work available at URL: vol35 2 3.html
review text: It is a famous problem: ``When is the quotient semigroup \(\frac{S}{\theta}\) with the quotient topology a topological semigroup?''. Here, \(S\) is a Hausdorff topological semigroup and \(\theta\) is a closed congruence on \(S\). This problem was studied by Wallace, and later by Lawson and Madison. Almost all the works about this question used some strong topological assumptions and they rarely used the algebraic structures of topological semigroups. However, the author claims that he considers both of these structures for a complete answer. He investigates conditions which are closely related to the ideals and topological structures of \(S\). First, he gives a necessary and sufficient condition on \(S\) and a closed ideal \(I\) of \(S\) such that \(\frac{S}{I}\) is a \(\kappa_\omega\)-space, then he uses this result to generalize Lawson and Madison's well known theorem.
Mathematics Subject Classification ID: 22A15
Mathematics Subject Classification ID: 54D50
zbMATH DE Number: 6029716
zbMATH Keywords: topological semigroup
zbMATH Keywords: topological congruence
zbMATH Keywords: quotient topology
zbMATH Keywords: \(\kappa_\omega\)-space
reviewed by: M. Akbari Tootkaboni
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6029716