Open subgroups, compact subgroups and Binz-Butzmann reflexivity
type: Item
instance of: scholarly article
title: Open subgroups, compact subgroups and Binz-Butzmann reflexivity
zbMATH Open document ID: 0892.43003
DOI: 10.1016/0166-8641(96)00015-6
author: M. Bruguera
author: E. Martín-Peinador
published in: Topology and its Applications
publication date: 1998-08-03T00:00:00Z
review text: The authors investigate the duality of Abelian convergence groups (in the sense of E. Binz and H. Butzmann). It is shown that if an Abelian topological group \(G\) (which in an obvious way is a convergence group) contains an open subgroup \(A\), then \(G\) is convergence reflexive (\(BB\)-reflexive, in the terminology of the present paper) iff \(A\) is \(BB\)-reflexive. Next, if the characters on an Abelian topological group \(G\) separate points and \(K\) is a compact subgroup of \(G\), then \(G\) is \(BB\)-reflexive iff \(G/K\) is \(BB\)-reflexive.
Mathematics Subject Classification ID: 43A40
Mathematics Subject Classification ID: 20K27
Mathematics Subject Classification ID: 22A05
zbMATH DE Number: 937144
zbMATH Keywords: Binz-Butzmann reflexivity
zbMATH Keywords: \(BB\)-reflexive
zbMATH Keywords: Abelian topological group
zbMATH Keywords: convergence reflexive
zbMATH Keywords: characters
reviewed by: Michael Megrelishvili
MaRDI profile type: Publication
full work available at URL: 0166-8641(96)00015-6
OpenAlex ID: W2009325285
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description: scientific article; zbMATH DE number 937144