Admissible topologies for groups of homeomorphisms and substitutions of groups of \(G\)-spaces
type: Item
instance of: scholarly article
title: Admissible topologies for groups of homeomorphisms and substitutions of groups of \(G\)-spaces
zbMATH Open document ID: 1452.54022
published in: Topology and its Applications
publication date: 2020-04-07T00:00:00Z
review text: The group of homeomorphisms in the discrete topology acts continuously and transitively on a homogeneous space \(X\). This paper aims at substituting the discrete acting group of a \(G\)-space by the quotient group with respect to the kernel of action, which would preserve various properties (transitivity, being a coset space, preserving a fixed equuniformity in case of \(G\)-Tychonoff space) of actions (Theorem 3.1). Such substitution is interesting from the perspective of investigating metrizability of phase spaces (Theorem 3.27) and deriving bounds on cardinal invariants of acting groups with admissible topologies (Theorem 3.12, 3.13). The authors exploit the product structure of the class of \(\mathcal{G}\)-range topological groups and the presence of a uniform structure on \(G\)-spaces to achieve their goals.
reviewed by: Kateryna Pavlyk
Mathematics Subject Classification ID: 54H15
Mathematics Subject Classification ID: 57S05
Mathematics Subject Classification ID: 22F30
Mathematics Subject Classification ID: 54D35
zbMATH DE Number: 7187680
zbMATH Keywords: homogeneity
zbMATH Keywords: topological group
zbMATH Keywords: \(G\)-space
zbMATH Keywords: uniformity
zbMATH Keywords: completion
author: A. Karassev
author: K. L. Kozlov
MaRDI profile type: Publication
full work available at URL: j.topol.2019.107033
OpenAlex ID: W2999064986
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DOI: 10.1016/J.TOPOL.2019.107033
description: scientific article; zbMATH DE number 7187680