Quasi-Metric Properties of the Dual Cone of an Asymmetric Normed Space

[EN] We obtain some quasi-metric properties of the dual cone of an asymmetric normed space. Thus, we prove that it is balanced, and hence its topology is completely regular. We also prove that it is complete in the sense of D. Doitchinov. These results generalize those obtained by Romaguera et al. i...

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Autor: Alegre Gil, Maria Carmen|||0000-0002-1004-4248
Tipo de recurso: artículo
Fecha de publicación:2022
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:10251/194433
Acceso en línea:https://riunet.upv.es/handle/10251/194433
Access Level:acceso abierto
Palabra clave:Quasi-metric
Asymmetric norm
Asymmetric normed linear space
Cone
Semicontinuous linear map
MATEMATICA APLICADA
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repository_id_str
spelling Quasi-Metric Properties of the Dual Cone of an Asymmetric Normed SpaceAlegre Gil, Maria Carmen|||0000-0002-1004-4248Quasi-metricAsymmetric normAsymmetric normed linear spaceConeSemicontinuous linear mapMATEMATICA APLICADA[EN] We obtain some quasi-metric properties of the dual cone of an asymmetric normed space. Thus, we prove that it is balanced, and hence its topology is completely regular. We also prove that it is complete in the sense of D. Doitchinov. These results generalize those obtained by Romaguera et al. in [18] because, in our study, the asymmetric normed space does not necessarily satisfy the T1 axiom. Moreover, we provide a class of asymmetric normed spaces whose dual cones are right K-sequentially complete. Finally, we represent an arbitrary asymmetric normed space as a function space by using the unit ball of its dual space.Springer-VerlagDepartamento de Matemática AplicadaInstituto Universitario de Matemática Pura y AplicadaEscuela Técnica Superior de Ingeniería InformáticaRepositorio Institucional de la Universitat Politècnica de València Riunet20222022-08-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/194433reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1944332026-06-13T07:49:27Z
dc.title.none.fl_str_mv Quasi-Metric Properties of the Dual Cone of an Asymmetric Normed Space
title Quasi-Metric Properties of the Dual Cone of an Asymmetric Normed Space
spellingShingle Quasi-Metric Properties of the Dual Cone of an Asymmetric Normed Space
Alegre Gil, Maria Carmen|||0000-0002-1004-4248
Quasi-metric
Asymmetric norm
Asymmetric normed linear space
Cone
Semicontinuous linear map
MATEMATICA APLICADA
title_short Quasi-Metric Properties of the Dual Cone of an Asymmetric Normed Space
title_full Quasi-Metric Properties of the Dual Cone of an Asymmetric Normed Space
title_fullStr Quasi-Metric Properties of the Dual Cone of an Asymmetric Normed Space
title_full_unstemmed Quasi-Metric Properties of the Dual Cone of an Asymmetric Normed Space
title_sort Quasi-Metric Properties of the Dual Cone of an Asymmetric Normed Space
dc.creator.none.fl_str_mv Alegre Gil, Maria Carmen|||0000-0002-1004-4248
author Alegre Gil, Maria Carmen|||0000-0002-1004-4248
author_facet Alegre Gil, Maria Carmen|||0000-0002-1004-4248
author_role author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Instituto Universitario de Matemática Pura y Aplicada
Escuela Técnica Superior de Ingeniería Informática
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Quasi-metric
Asymmetric norm
Asymmetric normed linear space
Cone
Semicontinuous linear map
MATEMATICA APLICADA
topic Quasi-metric
Asymmetric norm
Asymmetric normed linear space
Cone
Semicontinuous linear map
MATEMATICA APLICADA
description [EN] We obtain some quasi-metric properties of the dual cone of an asymmetric normed space. Thus, we prove that it is balanced, and hence its topology is completely regular. We also prove that it is complete in the sense of D. Doitchinov. These results generalize those obtained by Romaguera et al. in [18] because, in our study, the asymmetric normed space does not necessarily satisfy the T1 axiom. Moreover, we provide a class of asymmetric normed spaces whose dual cones are right K-sequentially complete. Finally, we represent an arbitrary asymmetric normed space as a function space by using the unit ball of its dual space.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-08-01
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/10251/194433
url https://riunet.upv.es/handle/10251/194433
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
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
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
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer-Verlag
publisher.none.fl_str_mv Springer-Verlag
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 15,300719

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