Open subgroups, compact subgroups amd Binz-Butzmannn reflexivity

A number of attempts to extend Pontryagin duality theory to categories of groups larger than that of locally compact abelian groups have been made using different approaches. The extension to the category of topological abelian groups created the concept of reflexive group. In this paper we deal wit...

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Detalles Bibliográficos
Autores: Martín Peinador, Elena, Bruguera Padró, M. Montserrat
Tipo de recurso: artículo
Fecha de publicación:1996
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/57058
Acceso en línea:https://hdl.handle.net/20.500.14352/57058
Access Level:acceso abierto
Palabra clave:515.1
Reflexive group
Continuous convergence structure
Character
Dual group
Topología
1210 Topología
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spelling Open subgroups, compact subgroups amd Binz-Butzmannn reflexivityMartín Peinador, ElenaBruguera Padró, M. Montserrat515.1Reflexive groupContinuous convergence structureCharacterDual groupTopología1210 TopologíaA number of attempts to extend Pontryagin duality theory to categories of groups larger than that of locally compact abelian groups have been made using different approaches. The extension to the category of topological abelian groups created the concept of reflexive group. In this paper we deal with the extension of Pontryagin duality to the category of convergence abelian groups. Reflexivity in this category was defined and studied by E. Binz and H. Butzmann. A convergence group is reflexive (subsequently called BB-reflexive by us in our work) if the canonical embedding into the bidual is a convergence isomorphism. Topological abelian groups are, in an obvious way, convergence groups; therefore it is natural to compare reflexivity and BB-reflexivity for them. Chasco and Martín-Peinador (1994) show that these two notions are independent. However some properties of reflexive groups also hold for BB-reflexive groups, and the purpose of this paper is to show two of them. Namely, we prove that if an abelian topological group G contains an open subgroup A, then G is BB-reflexive if and only if A is BB-reflexive. Next, if G has sufficiently many continuous characters and K is a compact subgroup of G, then G is BB-reflexive if and only if G/K is BB-reflexive.Elsevier ScienceUniversidad Complutense de Madrid19961996-08-2719961996-08-27journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/57058reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/570582026-06-02T12:44:21Z
dc.title.none.fl_str_mv Open subgroups, compact subgroups amd Binz-Butzmannn reflexivity
title Open subgroups, compact subgroups amd Binz-Butzmannn reflexivity
spellingShingle Open subgroups, compact subgroups amd Binz-Butzmannn reflexivity
Martín Peinador, Elena
515.1
Reflexive group
Continuous convergence structure
Character
Dual group
Topología
1210 Topología
title_short Open subgroups, compact subgroups amd Binz-Butzmannn reflexivity
title_full Open subgroups, compact subgroups amd Binz-Butzmannn reflexivity
title_fullStr Open subgroups, compact subgroups amd Binz-Butzmannn reflexivity
title_full_unstemmed Open subgroups, compact subgroups amd Binz-Butzmannn reflexivity
title_sort Open subgroups, compact subgroups amd Binz-Butzmannn reflexivity
dc.creator.none.fl_str_mv Martín Peinador, Elena
Bruguera Padró, M. Montserrat
author Martín Peinador, Elena
author_facet Martín Peinador, Elena
Bruguera Padró, M. Montserrat
author_role author
author2 Bruguera Padró, M. Montserrat
author2_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 515.1
Reflexive group
Continuous convergence structure
Character
Dual group
Topología
1210 Topología
topic 515.1
Reflexive group
Continuous convergence structure
Character
Dual group
Topología
1210 Topología
description A number of attempts to extend Pontryagin duality theory to categories of groups larger than that of locally compact abelian groups have been made using different approaches. The extension to the category of topological abelian groups created the concept of reflexive group. In this paper we deal with the extension of Pontryagin duality to the category of convergence abelian groups. Reflexivity in this category was defined and studied by E. Binz and H. Butzmann. A convergence group is reflexive (subsequently called BB-reflexive by us in our work) if the canonical embedding into the bidual is a convergence isomorphism. Topological abelian groups are, in an obvious way, convergence groups; therefore it is natural to compare reflexivity and BB-reflexivity for them. Chasco and Martín-Peinador (1994) show that these two notions are independent. However some properties of reflexive groups also hold for BB-reflexive groups, and the purpose of this paper is to show two of them. Namely, we prove that if an abelian topological group G contains an open subgroup A, then G is BB-reflexive if and only if A is BB-reflexive. Next, if G has sufficiently many continuous characters and K is a compact subgroup of G, then G is BB-reflexive if and only if G/K is BB-reflexive.
publishDate 1996
dc.date.none.fl_str_mv 1996
1996-08-27
1996
1996-08-27
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/57058
url https://hdl.handle.net/20.500.14352/57058
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300724

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