The structure of the poset of regular topologies on a set

[EN] We study the subposet E3(X) of the lattice L1(X) of all T1-topologies on a set X, being the collections of all T3 topologies on X, with a view to deciding which elements of this partially ordered set have and which do not have immediate predecessors. We show that each regular topology which is...

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Detalles Bibliográficos
Autores: Alas, Ofelia T., Wilson, Richard G.
Tipo de recurso: artículo
Fecha de publicación:2011
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:10251/86961
Acceso en línea:https://riunet.upv.es/handle/10251/86961
Access Level:acceso abierto
Palabra clave:Lattice of T1-topologies
Poset of T3-topologies
Upper topology
Lower topology
R-closed space
R-minimal space
Submaximal space
Maximal R-closed space
Dispersed space
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spelling The structure of the poset of regular topologies on a setAlas, Ofelia T.Wilson, Richard G.Lattice of T1-topologiesPoset of T3-topologiesUpper topologyLower topologyR-closed spaceR-minimal spaceSubmaximal spaceMaximal R-closed spaceDispersed space[EN] We study the subposet E3(X) of the lattice L1(X) of all T1-topologies on a set X, being the collections of all T3 topologies on X, with a view to deciding which elements of this partially ordered set have and which do not have immediate predecessors. We show that each regular topology which is not R-closed does have such a predecessor and as a corollary we obtain a result of Costantini that each non-compact Tychonoff space has an immediate predecessor in E3. We also consider the problem of when an R-closed topology is maximal R-closed.Research supported by Programa Integral de Fortalecimiento Institucional (PIFI), grant no. 34536-55 (México) and Fundaçãao de Amparo a Pesquisa do Estado de São Paulo (Brasil). The second author wishes to thank the Departament de Matem`atiques de la Universitat Jaume I for support from Pla 2009 de Promoció de la Investigació, Fundació Bancaixa, Castelló, during the preparation of the final version of this paper.Universitat Politècnica de ValènciaSecretaría de Educación Pública, MéxicoFundação de Amparo à Pesquisa do Estado de São PauloUniversitat Jaume IFundación BancajaRepositorio Institucional de la Universitat Politècnica de València Riunet20112011-04-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/86961reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengSecretaría de Educación Pública, México https://doi.org/10.13039/100010096 PIFI%2F34536-55open 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:10251/869612026-06-13T07:49:27Z
dc.title.none.fl_str_mv The structure of the poset of regular topologies on a set
title The structure of the poset of regular topologies on a set
spellingShingle The structure of the poset of regular topologies on a set
Alas, Ofelia T.
Lattice of T1-topologies
Poset of T3-topologies
Upper topology
Lower topology
R-closed space
R-minimal space
Submaximal space
Maximal R-closed space
Dispersed space
title_short The structure of the poset of regular topologies on a set
title_full The structure of the poset of regular topologies on a set
title_fullStr The structure of the poset of regular topologies on a set
title_full_unstemmed The structure of the poset of regular topologies on a set
title_sort The structure of the poset of regular topologies on a set
dc.creator.none.fl_str_mv Alas, Ofelia T.
Wilson, Richard G.
author Alas, Ofelia T.
author_facet Alas, Ofelia T.
Wilson, Richard G.
author_role author
author2 Wilson, Richard G.
author2_role author
dc.contributor.none.fl_str_mv Secretaría de Educación Pública, México
Fundação de Amparo à Pesquisa do Estado de São Paulo
Universitat Jaume I
Fundación Bancaja
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Lattice of T1-topologies
Poset of T3-topologies
Upper topology
Lower topology
R-closed space
R-minimal space
Submaximal space
Maximal R-closed space
Dispersed space
topic Lattice of T1-topologies
Poset of T3-topologies
Upper topology
Lower topology
R-closed space
R-minimal space
Submaximal space
Maximal R-closed space
Dispersed space
description [EN] We study the subposet E3(X) of the lattice L1(X) of all T1-topologies on a set X, being the collections of all T3 topologies on X, with a view to deciding which elements of this partially ordered set have and which do not have immediate predecessors. We show that each regular topology which is not R-closed does have such a predecessor and as a corollary we obtain a result of Costantini that each non-compact Tychonoff space has an immediate predecessor in E3. We also consider the problem of when an R-closed topology is maximal R-closed.
publishDate 2011
dc.date.none.fl_str_mv 2011
2011-04-01
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/10251/86961
url https://riunet.upv.es/handle/10251/86961
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Secretaría de Educación Pública, México https://doi.org/10.13039/100010096 PIFI%2F34536-55
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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