Open subgroups and Pontryagin duality
type: Item
instance of: scholarly article
title: Open subgroups and Pontryagin duality
zbMATH Open document ID: 0790.22001
DOI: 10.1007/BF02571709
published in: Mathematische Zeitschrift
publication date: 1994-06-15T00:00:00Z
full work available at URL: https://eudml.org/doc/174607
review text: An abelian topological group is called reflexive if the evaluation map \(G\to G\widehat{\phantom{x}}\widehat{\phantom{x}}\) is a topological isomorphism of \(G\) onto its second character group. We say that \(G\) is strongly reflexive if all closed subgroups and Hausdorff quotient groups of \(G\) and of \(G\widehat{\phantom{x}}\) are reflexive. Let \(A\) be an open subgroup of \(G\); it is proved that \(G\) is reflexive (resp. strongly reflexive) if and only if \(A\) is reflexive (resp. strongly reflexive).
Mathematics Subject Classification ID: 22A05
Mathematics Subject Classification ID: 43A40
zbMATH DE Number: 567397
zbMATH Keywords: Pontryagin duality
zbMATH Keywords: strongly reflexive groups
zbMATH Keywords: abelian topological group
zbMATH Keywords: character group
zbMATH Keywords: Hausdorff quotient groups
zbMATH Keywords: open subgroup
author: Wojciech Banaszczyk
author: M. J. Chasco
author: E. Martín-Peinador
MaRDI profile type: Publication
cites work: Additive subgroups of topological vector spaces
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cites work: Extensions of the Pontrjagin duality. I: Infinite products
cites work: k-Groups and Duality
description: scientific article; zbMATH DE number 567397