Sandwich-type characterization of completely regular spaces

[EN] All the higher separation axioms in topology, except for complete regularity, are known to have sandwich-type characterizations. This note provides a characterization of complete regularity in terms of inserting a continuous real-valued function. The known fact that each continuous real valued...

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Detalles Bibliográficos
Autores: Gutiérrez García, Javier, Kubiak, Tomasz
Tipo de recurso: artículo
Fecha de publicación:2007
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:10251/83070
Acceso en línea:https://riunet.upv.es/handle/10251/83070
Access Level:acceso abierto
Palabra clave:Insertion
Sandwich theorem
Insertion theorem
Completely regular space
Lower semicontinuous
Upper semicontinuous
Compact
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spelling Sandwich-type characterization of completely regular spacesGutiérrez García, JavierKubiak, TomaszInsertionSandwich theoremInsertion theoremCompletely regular spaceLower semicontinuousUpper semicontinuousCompact[EN] All the higher separation axioms in topology, except for complete regularity, are known to have sandwich-type characterizations. This note provides a characterization of complete regularity in terms of inserting a continuous real-valued function. The known fact that each continuous real valued function on a compact subset o fa Tychonoff space has a continuous extension to the whole space is obtained as a corollary.This research was supported by the Ministry of Education and Science of Spain and FEDER under grant MTM2006-14925-C02-02.Universitat Politècnica de ValènciaMinisterio de Educación y CienciaUniversidad del País Vasco/Euskal Herriko UnibertsitateaRepositorio Institucional de la Universitat Politècnica de València Riunet20072007-10-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/83070reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengMinisterio de Educación y Ciencia https://doi.org/10.13039/501100008743 MTM2006-14925-C02-02 METODOS TOPOLOGICOS EN EL ESTUDIO DE FUNCIONES CON VALORES EN DOMINIOS DE COMPUTACION Y (CASI-)UNIFORMIDADES FUZZY.UPV%2FEHU UPV%2FEHU UPV05%2F01open 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:10251/830702026-06-13T07:49:27Z
dc.title.none.fl_str_mv Sandwich-type characterization of completely regular spaces
title Sandwich-type characterization of completely regular spaces
spellingShingle Sandwich-type characterization of completely regular spaces
Gutiérrez García, Javier
Insertion
Sandwich theorem
Insertion theorem
Completely regular space
Lower semicontinuous
Upper semicontinuous
Compact
title_short Sandwich-type characterization of completely regular spaces
title_full Sandwich-type characterization of completely regular spaces
title_fullStr Sandwich-type characterization of completely regular spaces
title_full_unstemmed Sandwich-type characterization of completely regular spaces
title_sort Sandwich-type characterization of completely regular spaces
dc.creator.none.fl_str_mv Gutiérrez García, Javier
Kubiak, Tomasz
author Gutiérrez García, Javier
author_facet Gutiérrez García, Javier
Kubiak, Tomasz
author_role author
author2 Kubiak, Tomasz
author2_role author
dc.contributor.none.fl_str_mv Ministerio de Educación y Ciencia
Universidad del País Vasco/Euskal Herriko Unibertsitatea
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Insertion
Sandwich theorem
Insertion theorem
Completely regular space
Lower semicontinuous
Upper semicontinuous
Compact
topic Insertion
Sandwich theorem
Insertion theorem
Completely regular space
Lower semicontinuous
Upper semicontinuous
Compact
description [EN] All the higher separation axioms in topology, except for complete regularity, are known to have sandwich-type characterizations. This note provides a characterization of complete regularity in terms of inserting a continuous real-valued function. The known fact that each continuous real valued function on a compact subset o fa Tychonoff space has a continuous extension to the whole space is obtained as a corollary.
publishDate 2007
dc.date.none.fl_str_mv 2007
2007-10-01
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/10251/83070
url https://riunet.upv.es/handle/10251/83070
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Educación y Ciencia https://doi.org/10.13039/501100008743 MTM2006-14925-C02-02 METODOS TOPOLOGICOS EN EL ESTUDIO DE FUNCIONES CON VALORES EN DOMINIOS DE COMPUTACION Y (CASI-)UNIFORMIDADES FUZZY.
UPV%2FEHU UPV%2FEHU UPV05%2F01
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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score 15,300724

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