On partitions of groups into dense subsets
type: Item
instance of: scholarly article
title: On partitions of groups into dense subsets
zbMATH Open document ID: 1016.22001
DOI: 10.1016/S0166-8641(02)00093-7
author: Yevhen Zelenyuk
published in: Topology and its Applications
publication date: 2003-04-02T00:00:00Z
review text: A group is called absolutely resolvable (absolutely \(\omega\)-resolvable) if it can be partitioned into two (into \(\omega)\) subsets dense in any nondiscrete group topology. The author proves the basic theorems: (1) Every countable \(\omega\)-irresolvable topological group contains an open Boolean subgroup. (2) Every countable group with finitely many elements of order 2, that can be embedded in a compact topological group, is absolutely \(\omega\)-resolvable.
Mathematics Subject Classification ID: 22A05
Mathematics Subject Classification ID: 22A30
Mathematics Subject Classification ID: 54A05
Mathematics Subject Classification ID: 54H11
zbMATH DE Number: 1891215
zbMATH Keywords: resolvability
zbMATH Keywords: local left topological group
zbMATH Keywords: local automorphism
zbMATH Keywords: topological group
reviewed by: Bohumil František Šmarda
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1891215