Enveloping action: convergence spaces
type: Item
instance of: scholarly article
title: Enveloping action: convergence spaces
zbMATH Open document ID: 1506.54002
author: Bernd Losert
author: Gary Richardson
published in: Mathematica Slovaca
publication date: 2022-12-08T00:00:00Z
review text: In this paper the authors point out that quotient maps are central to the development of partial actions. Hereby, a partial action $\alpha$ of a topological group $G$ on a topological space is subject to certain axioms defined in the past. It is known that $\alpha$ is induced by a so-called enveloping action on a suitable chosen topological space $Y$. The topology on $Y$ is the quotient topology determined by an equivalence relation on $G\times Y$. Since in TOP quotient maps are neither productive nor hereditary certain difficulties are encountered in proving. Thus, the authors discuss a partial action and its enveloping action in the larger category CS of Kent convergence spaces and continuous maps which is cartesian closed and extensional and where fewer constraints are required. By using strongly quotient maps it is shown that they are invariant when passing to the enveloping action space. Furthermore, the enveloping action space may fail to be Hausdorff even when the original space is Hausdorff, but in that case an associated Hausdorff enveloping action space and the extension of quotients are presented.
reviewed by: Dieter Leseberg
Mathematics Subject Classification ID: 54A20
Mathematics Subject Classification ID: 54A05
Mathematics Subject Classification ID: 54B15
Mathematics Subject Classification ID: 54D10
Mathematics Subject Classification ID: 54H11
Mathematics Subject Classification ID: 54H15
zbMATH DE Number: 7629498
zbMATH Keywords: partial action
zbMATH Keywords: enveloping action
zbMATH Keywords: quotient map
zbMATH Keywords: convergence space
zbMATH Keywords: Kent convergence space
zbMATH Keywords: strongly quotient map
zbMATH Keywords: convergence group
zbMATH Keywords: Hausdorff property
MaRDI profile type: Publication
full work available at URL: ms-2022-0114
OpenAlex ID: W4313213831
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DOI: 10.1515/MS-2022-0114
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description: scientific article; zbMATH DE number 7629498