α-sober spaces via the orthogonal closure operator

Detalhes bibliográficos
Autor(a) principal: Sousa, Lurdes
Data de Publicação: 1996
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.19/2852
Resumo: Each ordinal alpha equipped with the upper topology is a T0-space. It is well known that for alpha=2 the reflective hull of alpha in Top0 is the subcategory of sober spaces. Here, we define alpha-sober space for every ordinal alpha in such a way that the reflective hull of alpha in Top0 is the subcategory of alpha-sober spaces. Moreover, we obtain an order-preserving bijective correspondence between a proper class of ordinals and the corresponding (epi)reflective hulls. Our main tool is the concept of orthogonal closure operator, introduced by the authour in a previous paper.
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spelling α-sober spaces via the orthogonal closure operatororthogonal closure operatorreflective hullalpha-sober spaceEach ordinal alpha equipped with the upper topology is a T0-space. It is well known that for alpha=2 the reflective hull of alpha in Top0 is the subcategory of sober spaces. Here, we define alpha-sober space for every ordinal alpha in such a way that the reflective hull of alpha in Top0 is the subcategory of alpha-sober spaces. Moreover, we obtain an order-preserving bijective correspondence between a proper class of ordinals and the corresponding (epi)reflective hulls. Our main tool is the concept of orthogonal closure operator, introduced by the authour in a previous paper.R. LowenRepositório Científico do Instituto Politécnico de ViseuSousa, Lurdes2015-06-30T08:16:55Z19961996-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.19/2852eng0927-2852metadata only accessinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-01-16T15:26:10Zoai:repositorio.ipv.pt:10400.19/2852Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T16:41:58.494380Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv α-sober spaces via the orthogonal closure operator
title α-sober spaces via the orthogonal closure operator
spellingShingle α-sober spaces via the orthogonal closure operator
Sousa, Lurdes
orthogonal closure operator
reflective hull
alpha-sober space
title_short α-sober spaces via the orthogonal closure operator
title_full α-sober spaces via the orthogonal closure operator
title_fullStr α-sober spaces via the orthogonal closure operator
title_full_unstemmed α-sober spaces via the orthogonal closure operator
title_sort α-sober spaces via the orthogonal closure operator
author Sousa, Lurdes
author_facet Sousa, Lurdes
author_role author
dc.contributor.none.fl_str_mv Repositório Científico do Instituto Politécnico de Viseu
dc.contributor.author.fl_str_mv Sousa, Lurdes
dc.subject.por.fl_str_mv orthogonal closure operator
reflective hull
alpha-sober space
topic orthogonal closure operator
reflective hull
alpha-sober space
description Each ordinal alpha equipped with the upper topology is a T0-space. It is well known that for alpha=2 the reflective hull of alpha in Top0 is the subcategory of sober spaces. Here, we define alpha-sober space for every ordinal alpha in such a way that the reflective hull of alpha in Top0 is the subcategory of alpha-sober spaces. Moreover, we obtain an order-preserving bijective correspondence between a proper class of ordinals and the corresponding (epi)reflective hulls. Our main tool is the concept of orthogonal closure operator, introduced by the authour in a previous paper.
publishDate 1996
dc.date.none.fl_str_mv 1996
1996-01-01T00:00:00Z
2015-06-30T08:16:55Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.19/2852
url http://hdl.handle.net/10400.19/2852
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0927-2852
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rights_invalid_str_mv metadata only access
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dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv R. Lowen
publisher.none.fl_str_mv R. Lowen
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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