Probabilistic uniformities of uniform spaces

[EN] Usually, fuzzy metric spaces are endowed with crisp topologies or crisp uniformities. Nevertheless, some authors have shown how to construct in this context different kinds of fuzzy uniformities like a Hutton [0, 1]- quasi-uniformity or a probabilistic uniformity. In 2010, J. Guti´errez Garc´ıa...

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Autores: Rodríguez López, Jesús|||0000-0001-5141-9977, Romaguera Bonilla, Salvador|||0000-0001-7857-6139, Sanchis, Manuel
Tipo de recurso: capítulo de libro
Fecha de publicación:2017
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:10251/128037
Acceso en línea:https://riunet.upv.es/handle/10251/128037
Access Level:acceso abierto
Palabra clave:Fuzzy metric space
Fuzzy gauge base
Probabilistic uniformity
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spelling Probabilistic uniformities of uniform spacesRodríguez López, Jesús|||0000-0001-5141-9977Romaguera Bonilla, Salvador|||0000-0001-7857-6139Sanchis, ManuelFuzzy metric spaceFuzzy gauge baseProbabilistic uniformity[EN] Usually, fuzzy metric spaces are endowed with crisp topologies or crisp uniformities. Nevertheless, some authors have shown how to construct in this context different kinds of fuzzy uniformities like a Hutton [0, 1]- quasi-uniformity or a probabilistic uniformity. In 2010, J. Guti´errez Garc´ıa, S. Romaguera and M. Sanchis [7] proved that the category of uniform spaces is isomorphic to a category whose objects are sets endowed with a fuzzy uniform structure, i. e. a family of fuzzy pseudometrics satisfying certain conditions. We will show here that, by means of this isomorphism, we can obtain several methods to endow a uniform space with a probabilistic uniformity. Furthermore, we obtain a factorization of some functors introduced in [6].The first and third authors are supported by the grant MTM2015-64373-P (MINECO/FEDER, UE).Editorial Universitat Politècnica de ValènciaDepartamento de Matemática AplicadaEscuela Técnica Superior de Ingeniería Aeroespacial y Diseño IndustrialInstituto Universitario de Matemática Pura y AplicadaMinisterio de Economía y CompetitividadRepositorio Institucional de la Universitat Politècnica de València Riunet20172017-10-23book parthttp://purl.org/coar/resource_type/c_3248VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/bookPartapplication/pdfhttps://riunet.upv.es/handle/10251/128037reponame: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 MTM2015-64373-P HIPERESPACIOS, ESTRUCTURAS DIFUSAS Y ASIMETRICAS. APLICACIONES A CIENCIA DE LA COMPUTACION Y AL FILTRADO DE IMAGENES.open 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:10251/1280372026-06-13T07:49:27Z
dc.title.none.fl_str_mv Probabilistic uniformities of uniform spaces
title Probabilistic uniformities of uniform spaces
spellingShingle Probabilistic uniformities of uniform spaces
Rodríguez López, Jesús|||0000-0001-5141-9977
Fuzzy metric space
Fuzzy gauge base
Probabilistic uniformity
title_short Probabilistic uniformities of uniform spaces
title_full Probabilistic uniformities of uniform spaces
title_fullStr Probabilistic uniformities of uniform spaces
title_full_unstemmed Probabilistic uniformities of uniform spaces
title_sort Probabilistic uniformities of uniform spaces
dc.creator.none.fl_str_mv Rodríguez López, Jesús|||0000-0001-5141-9977
Romaguera Bonilla, Salvador|||0000-0001-7857-6139
Sanchis, Manuel
author Rodríguez López, Jesús|||0000-0001-5141-9977
author_facet Rodríguez López, Jesús|||0000-0001-5141-9977
Romaguera Bonilla, Salvador|||0000-0001-7857-6139
Sanchis, Manuel
author_role author
author2 Romaguera Bonilla, Salvador|||0000-0001-7857-6139
Sanchis, Manuel
author2_role author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Escuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial
Instituto Universitario de Matemática Pura y Aplicada
Ministerio de Economía y Competitividad
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Fuzzy metric space
Fuzzy gauge base
Probabilistic uniformity
topic Fuzzy metric space
Fuzzy gauge base
Probabilistic uniformity
description [EN] Usually, fuzzy metric spaces are endowed with crisp topologies or crisp uniformities. Nevertheless, some authors have shown how to construct in this context different kinds of fuzzy uniformities like a Hutton [0, 1]- quasi-uniformity or a probabilistic uniformity. In 2010, J. Guti´errez Garc´ıa, S. Romaguera and M. Sanchis [7] proved that the category of uniform spaces is isomorphic to a category whose objects are sets endowed with a fuzzy uniform structure, i. e. a family of fuzzy pseudometrics satisfying certain conditions. We will show here that, by means of this isomorphism, we can obtain several methods to endow a uniform space with a probabilistic uniformity. Furthermore, we obtain a factorization of some functors introduced in [6].
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-10-23
dc.type.none.fl_str_mv book part
http://purl.org/coar/resource_type/c_3248
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/bookPart
format bookPart
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/128037
url https://riunet.upv.es/handle/10251/128037
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 MTM2015-64373-P HIPERESPACIOS, ESTRUCTURAS DIFUSAS Y ASIMETRICAS. APLICACIONES A CIENCIA DE LA COMPUTACION Y AL FILTRADO DE IMAGENES.
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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