Joins of closed sublocales
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10316/90477 |
Resumo: | Sublocales that are joins of closed ones constitute a frame S_Vc(L) embedded as a sup-sublattice into the coframe S(L) of sublocales of L. We prove that in the case of subfit L it is a subcolocale of S(L), that it is then a Boolean algebra and in fact precisely the Booleanization of S(L). In case of a T_1-space X, S_Vc(\Omega(X)) picks precisely the sublocales corresponding to induced subspaces. In linear L and more generally if L is also a coframe, S_Vc(L) is both a frame and a coframe, but with trivial exceptions not Boolean and not a subcolocale of S(L). |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
spelling |
Joins of closed sublocalesFrame, locale, sublocale, nucleus, sublocale lattice, coframe, open sublocale, closed sublocale, T1-space, induced subspace, subfit frame, fit frame, Booleanization.Sublocales that are joins of closed ones constitute a frame S_Vc(L) embedded as a sup-sublattice into the coframe S(L) of sublocales of L. We prove that in the case of subfit L it is a subcolocale of S(L), that it is then a Boolean algebra and in fact precisely the Booleanization of S(L). In case of a T_1-space X, S_Vc(\Omega(X)) picks precisely the sublocales corresponding to induced subspaces. In linear L and more generally if L is also a coframe, S_Vc(L) is both a frame and a coframe, but with trivial exceptions not Boolean and not a subcolocale of S(L).University of Houston20192024-12-30T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/90477http://hdl.handle.net/10316/90477enghttps://www.math.uh.edu/~hjm/Vol45-1.htmlPicado, JorgePultr, AlešTozzi, Annainfo:eu-repo/semantics/embargoedAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-10-27T10:57:10Zoai:estudogeral.uc.pt:10316/90477Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:10:36.333245Repositório 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 |
Joins of closed sublocales |
title |
Joins of closed sublocales |
spellingShingle |
Joins of closed sublocales Picado, Jorge Frame, locale, sublocale, nucleus, sublocale lattice, coframe, open sublocale, closed sublocale, T1-space, induced subspace, subfit frame, fit frame, Booleanization. |
title_short |
Joins of closed sublocales |
title_full |
Joins of closed sublocales |
title_fullStr |
Joins of closed sublocales |
title_full_unstemmed |
Joins of closed sublocales |
title_sort |
Joins of closed sublocales |
author |
Picado, Jorge |
author_facet |
Picado, Jorge Pultr, Aleš Tozzi, Anna |
author_role |
author |
author2 |
Pultr, Aleš Tozzi, Anna |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Picado, Jorge Pultr, Aleš Tozzi, Anna |
dc.subject.por.fl_str_mv |
Frame, locale, sublocale, nucleus, sublocale lattice, coframe, open sublocale, closed sublocale, T1-space, induced subspace, subfit frame, fit frame, Booleanization. |
topic |
Frame, locale, sublocale, nucleus, sublocale lattice, coframe, open sublocale, closed sublocale, T1-space, induced subspace, subfit frame, fit frame, Booleanization. |
description |
Sublocales that are joins of closed ones constitute a frame S_Vc(L) embedded as a sup-sublattice into the coframe S(L) of sublocales of L. We prove that in the case of subfit L it is a subcolocale of S(L), that it is then a Boolean algebra and in fact precisely the Booleanization of S(L). In case of a T_1-space X, S_Vc(\Omega(X)) picks precisely the sublocales corresponding to induced subspaces. In linear L and more generally if L is also a coframe, S_Vc(L) is both a frame and a coframe, but with trivial exceptions not Boolean and not a subcolocale of S(L). |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019 2024-12-30T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10316/90477 http://hdl.handle.net/10316/90477 |
url |
http://hdl.handle.net/10316/90477 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://www.math.uh.edu/~hjm/Vol45-1.html |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/embargoedAccess |
eu_rights_str_mv |
embargoedAccess |
dc.publisher.none.fl_str_mv |
University of Houston |
publisher.none.fl_str_mv |
University of Houston |
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 instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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 |
repository.mail.fl_str_mv |
|
_version_ |
1799134000397156352 |