A domain-theoretic approach to fuzzy metric spaces

We introduce a partial order (sic)(M) on the set BX of formal balls of a fuzzy metric space (X, M, Lambda) in the sense of Kramosil and Michalek, and discuss some of its properties. We also characterize when the poset (BX, (sic)(M)) is a continuous domain by means of a new notion of fuzzy metric com...

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Autores: Ricarte Moreno, Luis Alberto, Romaguera Bonilla, Salvador|||0000-0001-7857-6139
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:10251/55700
Acceso en línea:https://riunet.upv.es/handle/10251/55700
Access Level:acceso abierto
Palabra clave:Fuzzy metric space
Formal ball
Poset
Continuous domain
Standard complete
MATEMATICA APLICADA
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spelling A domain-theoretic approach to fuzzy metric spacesRicarte Moreno, Luis AlbertoRomaguera Bonilla, Salvador|||0000-0001-7857-6139Fuzzy metric spaceFormal ballPosetContinuous domainStandard completeMATEMATICA APLICADAWe introduce a partial order (sic)(M) on the set BX of formal balls of a fuzzy metric space (X, M, Lambda) in the sense of Kramosil and Michalek, and discuss some of its properties. We also characterize when the poset (BX, (sic)(M)) is a continuous domain by means of a new notion of fuzzy metric completeness introduced here. The well-known theorem of Edalat and Heckmann that a metric space is complete if and only if its poset of formal balls is a continuous domain, is deduced from our characterizationSupported by the Ministry of Economy and Competitiveness of Spain, under grant MTM2012-37894-C02-01.ElsevierInstituto Universitario de Matemática Pura y AplicadaMinisterio de Economía y CompetitividadInstituto de Salud Carlos IIICentro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y NanomedicinaRepositorio Institucional de la Universitat Politècnica de València Riunet20142014-02-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/55700reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengMinisterio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2012-37894-C02-01 METODOS TOPOLOGICOS EN HIPERESPACIOS Y MULTIFUNCIONES CONTRACTIVAS. CASI-METRICAS Y DOMINIOS CUANTITATIVOSopen 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:10251/557002026-06-13T07:49:27Z
dc.title.none.fl_str_mv A domain-theoretic approach to fuzzy metric spaces
title A domain-theoretic approach to fuzzy metric spaces
spellingShingle A domain-theoretic approach to fuzzy metric spaces
Ricarte Moreno, Luis Alberto
Fuzzy metric space
Formal ball
Poset
Continuous domain
Standard complete
MATEMATICA APLICADA
title_short A domain-theoretic approach to fuzzy metric spaces
title_full A domain-theoretic approach to fuzzy metric spaces
title_fullStr A domain-theoretic approach to fuzzy metric spaces
title_full_unstemmed A domain-theoretic approach to fuzzy metric spaces
title_sort A domain-theoretic approach to fuzzy metric spaces
dc.creator.none.fl_str_mv Ricarte Moreno, Luis Alberto
Romaguera Bonilla, Salvador|||0000-0001-7857-6139
author Ricarte Moreno, Luis Alberto
author_facet Ricarte Moreno, Luis Alberto
Romaguera Bonilla, Salvador|||0000-0001-7857-6139
author_role author
author2 Romaguera Bonilla, Salvador|||0000-0001-7857-6139
author2_role author
dc.contributor.none.fl_str_mv Instituto Universitario de Matemática Pura y Aplicada
Ministerio de Economía y Competitividad
Instituto de Salud Carlos III
Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Fuzzy metric space
Formal ball
Poset
Continuous domain
Standard complete
MATEMATICA APLICADA
topic Fuzzy metric space
Formal ball
Poset
Continuous domain
Standard complete
MATEMATICA APLICADA
description We introduce a partial order (sic)(M) on the set BX of formal balls of a fuzzy metric space (X, M, Lambda) in the sense of Kramosil and Michalek, and discuss some of its properties. We also characterize when the poset (BX, (sic)(M)) is a continuous domain by means of a new notion of fuzzy metric completeness introduced here. The well-known theorem of Edalat and Heckmann that a metric space is complete if and only if its poset of formal balls is a continuous domain, is deduced from our characterization
publishDate 2014
dc.date.none.fl_str_mv 2014
2014-02-01
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/10251/55700
url https://riunet.upv.es/handle/10251/55700
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2012-37894-C02-01 METODOS TOPOLOGICOS EN HIPERESPACIOS Y MULTIFUNCIONES CONTRACTIVAS. CASI-METRICAS Y DOMINIOS CUANTITATIVOS
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 Elsevier
publisher.none.fl_str_mv Elsevier
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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