Subgroups of paratopological groups and feebly compact groups

[EN] It is shown that if all countable subgroups of a semitopological group G are precompact, then G is also precompact and that the closure of an arbitrary subgroup of G is again a subgroup. We present a general method of refining the topology of a given commutative paratopological group G such tha...

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Detalles Bibliográficos
Autores: Fernández, Manuel, Tkachenko, Mikhail G.
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/43631
Acceso en línea:https://riunet.upv.es/handle/10251/43631
Access Level:acceso abierto
Palabra clave:Feebly compact
Precompact
Paratopological group
Subsemigroup
Topologically periodic
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spelling Subgroups of paratopological groups and feebly compact groupsFernández, ManuelTkachenko, Mikhail G.Feebly compactPrecompactParatopological groupSubsemigroupTopologically periodic[EN] It is shown that if all countable subgroups of a semitopological group G are precompact, then G is also precompact and that the closure of an arbitrary subgroup of G is again a subgroup. We present a general method of refining the topology of a given commutative paratopological group G such that the group G with the finer topology, say, σ is again a paratopological group containing a subgroup whose closure in (G, σ) is not a subgroup. It is also proved that a feebly compact paratopological group H is perfectly k-normal and that every Gδ-dense subspace of H is feebly compact.This author was supported by CONACyT of Mexico, grant CB-2012-01 178103.Editorial Universitat Politècnica de ValènciaConsejo Nacional de Ciencia y Tecnología, MéxicoRepositorio Institucional de la Universitat Politècnica de València Riunet20142014-10-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/43631reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengCONACyT CONACyT CB-2012-01-178103open accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/436312026-06-13T07:49:27Z
dc.title.none.fl_str_mv Subgroups of paratopological groups and feebly compact groups
title Subgroups of paratopological groups and feebly compact groups
spellingShingle Subgroups of paratopological groups and feebly compact groups
Fernández, Manuel
Feebly compact
Precompact
Paratopological group
Subsemigroup
Topologically periodic
title_short Subgroups of paratopological groups and feebly compact groups
title_full Subgroups of paratopological groups and feebly compact groups
title_fullStr Subgroups of paratopological groups and feebly compact groups
title_full_unstemmed Subgroups of paratopological groups and feebly compact groups
title_sort Subgroups of paratopological groups and feebly compact groups
dc.creator.none.fl_str_mv Fernández, Manuel
Tkachenko, Mikhail G.
author Fernández, Manuel
author_facet Fernández, Manuel
Tkachenko, Mikhail G.
author_role author
author2 Tkachenko, Mikhail G.
author2_role author
dc.contributor.none.fl_str_mv Consejo Nacional de Ciencia y Tecnología, México
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Feebly compact
Precompact
Paratopological group
Subsemigroup
Topologically periodic
topic Feebly compact
Precompact
Paratopological group
Subsemigroup
Topologically periodic
description [EN] It is shown that if all countable subgroups of a semitopological group G are precompact, then G is also precompact and that the closure of an arbitrary subgroup of G is again a subgroup. We present a general method of refining the topology of a given commutative paratopological group G such that the group G with the finer topology, say, σ is again a paratopological group containing a subgroup whose closure in (G, σ) is not a subgroup. It is also proved that a feebly compact paratopological group H is perfectly k-normal and that every Gδ-dense subspace of H is feebly compact.
publishDate 2014
dc.date.none.fl_str_mv 2014
2014-10-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/43631
url https://riunet.upv.es/handle/10251/43631
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv CONACyT CONACyT CB-2012-01-178103
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
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
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Editorial Universitat Politècnica de València
publisher.none.fl_str_mv Editorial Universitat Politècnica de València
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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