Preservation of completeness under mappings in asymmetric topology

[EN] The preservation of various completeness properties in the quasi-metric (and quasi-uniform) setting under open, closed and uniformly open mappings is investigated. In particular, it is noted that between quasi-uniform spaces the property that each costable filter has a cluster point is preserve...

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Detalhes bibliográficos
Autor: Künzi, Hans-Peter A.
Tipo de documento: artigo
Data de publicação:2000
País:España
Recursos:Universitat Politècnica de València (UPV)
Repositório:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglês
OAI Identifier:oai:riunet.upv.es:10251/81899
Acesso em linha:https://riunet.upv.es/handle/10251/81899
Access Level:Acceso aberto
Palavra-chave:Uniformly open mapping
Almost uniformly open mapping
Open mapping theorem
Quasi-metrizable
Left K-complete
Open mapping
Closed mapping
Supercomplete
Aronszajn space
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spelling Preservation of completeness under mappings in asymmetric topologyKünzi, Hans-Peter A.Uniformly open mappingAlmost uniformly open mappingOpen mapping theoremQuasi-metrizableLeft K-completeOpen mappingClosed mappingSupercompleteAronszajn space[EN] The preservation of various completeness properties in the quasi-metric (and quasi-uniform) setting under open, closed and uniformly open mappings is investigated. In particular, it is noted that between quasi-uniform spaces the property that each costable filter has a cluster point is preserved under uniformly open continuous surjections. Furthermore in the realm of quasi-uniform spaces conditions under which almost uniformly open mappings are uniformly open are given which generalize corresponding classical results for uniform spaces. As a by-product it is shown that a quasi-metrizable Moore space admits a left K-complete quasi-metric if and only if it is a complete Aronszajn space.This paper was written while the author was supported by the Swiss National Science Foundation under grant 2000-056811.99. He also acknowledges support during a visit to the University of Oxford by the Stiftung zur F orderung der wissenschaftlichen Forschung an der Universit at Bern.Universitat Politècnica de ValènciaSwiss National Science FoundationRepositorio Institucional de la Universitat Politècnica de València Riunet20002000-10-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/81899reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengSwiss National Science Foundation https://doi.org/10.13039/501100001711 2000-056811.99open 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:10251/818992026-06-13T07:49:27Z
dc.title.none.fl_str_mv Preservation of completeness under mappings in asymmetric topology
title Preservation of completeness under mappings in asymmetric topology
spellingShingle Preservation of completeness under mappings in asymmetric topology
Künzi, Hans-Peter A.
Uniformly open mapping
Almost uniformly open mapping
Open mapping theorem
Quasi-metrizable
Left K-complete
Open mapping
Closed mapping
Supercomplete
Aronszajn space
title_short Preservation of completeness under mappings in asymmetric topology
title_full Preservation of completeness under mappings in asymmetric topology
title_fullStr Preservation of completeness under mappings in asymmetric topology
title_full_unstemmed Preservation of completeness under mappings in asymmetric topology
title_sort Preservation of completeness under mappings in asymmetric topology
dc.creator.none.fl_str_mv Künzi, Hans-Peter A.
author Künzi, Hans-Peter A.
author_facet Künzi, Hans-Peter A.
author_role author
dc.contributor.none.fl_str_mv Swiss National Science Foundation
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Uniformly open mapping
Almost uniformly open mapping
Open mapping theorem
Quasi-metrizable
Left K-complete
Open mapping
Closed mapping
Supercomplete
Aronszajn space
topic Uniformly open mapping
Almost uniformly open mapping
Open mapping theorem
Quasi-metrizable
Left K-complete
Open mapping
Closed mapping
Supercomplete
Aronszajn space
description [EN] The preservation of various completeness properties in the quasi-metric (and quasi-uniform) setting under open, closed and uniformly open mappings is investigated. In particular, it is noted that between quasi-uniform spaces the property that each costable filter has a cluster point is preserved under uniformly open continuous surjections. Furthermore in the realm of quasi-uniform spaces conditions under which almost uniformly open mappings are uniformly open are given which generalize corresponding classical results for uniform spaces. As a by-product it is shown that a quasi-metrizable Moore space admits a left K-complete quasi-metric if and only if it is a complete Aronszajn space.
publishDate 2000
dc.date.none.fl_str_mv 2000
2000-10-01
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/10251/81899
url https://riunet.upv.es/handle/10251/81899
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Swiss National Science Foundation https://doi.org/10.13039/501100001711 2000-056811.99
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 15,301603

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