The groups of the semigroup of compact subsets of a topological group
type: Item
instance of: scholarly article
title: The groups of the semigroup of compact subsets of a topological group
zbMATH Open document ID: 0726.22004
DOI: 10.1007/BF02574254
author: Michael Gass
published in: Semigroup Forum
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/135098
review text: The compact subsets of a topological group G form a topological semigroup S(G) under set product and Vietoris topology. The author shows that the subgroups of S(G) are precisely the topological groups of the form H/E, where \(E\trianglelefteq H<G\), E is compact, and H/E has the quotient topology. Conditions are given for these subgroups to be open or closed. The author also points out that the Schützenberger group of a D-class of S(G) is topologically isomorphic to a section of G by a compact subgroup and the Schützenberger groups of S(G) are topological groups.
Mathematics Subject Classification ID: 22A15
Mathematics Subject Classification ID: 22A05
zbMATH DE Number: 4198344
zbMATH Keywords: compact subsets
zbMATH Keywords: topological semigroup
zbMATH Keywords: Vietoris topology
zbMATH Keywords: subgroups
zbMATH Keywords: topological groups
zbMATH Keywords: D-class
zbMATH Keywords: compact subgroup
zbMATH Keywords: Schützenberger groups
reviewed by: K. P. Shum
MaRDI profile type: Publication
cites work: Q5799920
cites work: Q3661823
cites work: Q3853827
cites work: Subgroups of the power semigroup of a group
cites work: Topologies on Spaces of Subsets
cites work: Q3758116
OpenAlex ID: W2058482693
description: scientific article; zbMATH DE number 4198344