Quantale-valued Cauchy tower spaces and completeness

[EN] Generalizing the concept of a probabilistic Cauchy space, we introduce quantale-valued Cauchy tower spaces. These spaces encompass quantale-valued metric spaces, quantale-valued uniform (convergence) tower spaces and quantale-valued convergence tower groups. For special choices of the quantale,...

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Detalles Bibliográficos
Autores: Jäger, Gunther, Ahsanullah, T. M. G.
Tipo de recurso: artículo
Fecha de publicación:2021
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:10251/173929
Acceso en línea:https://riunet.upv.es/handle/10251/173929
Access Level:acceso abierto
Palabra clave:Cauchy space
Quantale-valued metric space
Quantale-valued uniform convergence tower space
Completeness
Completion
Cauchy completeness
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spelling Quantale-valued Cauchy tower spaces and completenessJäger, GuntherAhsanullah, T. M. G.Cauchy spaceQuantale-valued metric spaceQuantale-valued uniform convergence tower spaceCompletenessCompletionCauchy completeness[EN] Generalizing the concept of a probabilistic Cauchy space, we introduce quantale-valued Cauchy tower spaces. These spaces encompass quantale-valued metric spaces, quantale-valued uniform (convergence) tower spaces and quantale-valued convergence tower groups. For special choices of the quantale, classical and probabilistic metric spaces are covered and probabilistic and approach Cauchy spaces arise. We also study completeness and completion in this setting and establish a connection to the Cauchy completeness of a quantale-valued metric space.Universitat Politècnica de ValènciaRepositorio Institucional de la Universitat Politècnica de València Riunet20212021-10-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/173929reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)Inglésengopen 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:10251/1739292026-06-13T07:49:27Z
dc.title.none.fl_str_mv Quantale-valued Cauchy tower spaces and completeness
title Quantale-valued Cauchy tower spaces and completeness
spellingShingle Quantale-valued Cauchy tower spaces and completeness
Jäger, Gunther
Cauchy space
Quantale-valued metric space
Quantale-valued uniform convergence tower space
Completeness
Completion
Cauchy completeness
title_short Quantale-valued Cauchy tower spaces and completeness
title_full Quantale-valued Cauchy tower spaces and completeness
title_fullStr Quantale-valued Cauchy tower spaces and completeness
title_full_unstemmed Quantale-valued Cauchy tower spaces and completeness
title_sort Quantale-valued Cauchy tower spaces and completeness
dc.creator.none.fl_str_mv Jäger, Gunther
Ahsanullah, T. M. G.
author Jäger, Gunther
author_facet Jäger, Gunther
Ahsanullah, T. M. G.
author_role author
author2 Ahsanullah, T. M. G.
author2_role author
dc.contributor.none.fl_str_mv Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Cauchy space
Quantale-valued metric space
Quantale-valued uniform convergence tower space
Completeness
Completion
Cauchy completeness
topic Cauchy space
Quantale-valued metric space
Quantale-valued uniform convergence tower space
Completeness
Completion
Cauchy completeness
description [EN] Generalizing the concept of a probabilistic Cauchy space, we introduce quantale-valued Cauchy tower spaces. These spaces encompass quantale-valued metric spaces, quantale-valued uniform (convergence) tower spaces and quantale-valued convergence tower groups. For special choices of the quantale, classical and probabilistic metric spaces are covered and probabilistic and approach Cauchy spaces arise. We also study completeness and completion in this setting and establish a connection to the Cauchy completeness of a quantale-valued metric space.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-10-01
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/10251/173929
url https://riunet.upv.es/handle/10251/173929
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
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 Universitat Politècnica de València
publisher.none.fl_str_mv 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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