Existence and number of maximal precompact topologies on Abelian groups
type: Item
instance of: scholarly article
title: Existence and number of maximal precompact topologies on Abelian groups
zbMATH Open document ID: 0706.22001
DOI: 10.1007/BF03322464
author: Fritz Schinkel
published in: Results in Mathematics
publication date: 1990-01-01T00:00:00Z
review text: A group topology on an Abelian group G is called maximal precompact iff it is an anti-atom in the lattice of all precompact group topologies on G. The author characterizes all Abelian groups admitting (Hausdorff) maximal precompact group topologies. For such groups he determines the number of p-maximal precompact (Hausdorff) group topologies. (The notion ``p-maximal'' is introduced in the paper.)
Mathematics Subject Classification ID: 22A05
Mathematics Subject Classification ID: 54A10
Mathematics Subject Classification ID: 54D30
Mathematics Subject Classification ID: 20K45
zbMATH DE Number: 4158969
zbMATH Keywords: lattice of precompact group topologies
zbMATH Keywords: Abelian groups
zbMATH Keywords: maximal precompact group topologies
reviewed by: Dieter Remus
MaRDI profile type: Publication
cites work: Topologies induced by groups of characters
cites work: Q5609457
cites work: Q5723435
cites work: On the structure of the lattice of group topologies
full work available at URL: https://doi.org/10.1007/bf03322464
OpenAlex ID: W2057120644
description: scientific article; zbMATH DE number 4158969