Entourages, Covers and Localic Groups
Autor(a) principal: | |
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Data de Publicação: | 2011 |
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/10316/43784 https://doi.org/10.1007/s10485-011-9254-3 |
Resumo: | Due to the nature of product in the category of locales, the entourage uniformities in the point-free context only mimic the classical Weil approach while the cover (Tukey type) ones can be viewed as an immediate extension. Nevertheless the resulting categories are concretely isomorphic. We present a transparent construction of this isomorphism, and apply it to the natural uniformities of localic groups. In particular we show that localic group homomorphisms are uniform, thus providing natural forgetful functors from the category of localic groups into any of the two categories of uniform locales. |
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Entourages, Covers and Localic GroupsDue to the nature of product in the category of locales, the entourage uniformities in the point-free context only mimic the classical Weil approach while the cover (Tukey type) ones can be viewed as an immediate extension. Nevertheless the resulting categories are concretely isomorphic. We present a transparent construction of this isomorphism, and apply it to the natural uniformities of localic groups. In particular we show that localic group homomorphisms are uniform, thus providing natural forgetful functors from the category of localic groups into any of the two categories of uniform locales.Springer2011info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/43784http://hdl.handle.net/10316/43784https://doi.org/10.1007/s10485-011-9254-3https://doi.org/10.1007/s10485-011-9254-3enghttps://link.springer.com/article/10.1007%2Fs10485-011-9254-3Picado, JorgePultr, Alešinfo: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:RCAAP2021-06-29T10:02:53Zoai:estudogeral.uc.pt:10316/43784Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:27.474605Repositório 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 |
Entourages, Covers and Localic Groups |
title |
Entourages, Covers and Localic Groups |
spellingShingle |
Entourages, Covers and Localic Groups Picado, Jorge |
title_short |
Entourages, Covers and Localic Groups |
title_full |
Entourages, Covers and Localic Groups |
title_fullStr |
Entourages, Covers and Localic Groups |
title_full_unstemmed |
Entourages, Covers and Localic Groups |
title_sort |
Entourages, Covers and Localic Groups |
author |
Picado, Jorge |
author_facet |
Picado, Jorge Pultr, Aleš |
author_role |
author |
author2 |
Pultr, Aleš |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Picado, Jorge Pultr, Aleš |
description |
Due to the nature of product in the category of locales, the entourage uniformities in the point-free context only mimic the classical Weil approach while the cover (Tukey type) ones can be viewed as an immediate extension. Nevertheless the resulting categories are concretely isomorphic. We present a transparent construction of this isomorphism, and apply it to the natural uniformities of localic groups. In particular we show that localic group homomorphisms are uniform, thus providing natural forgetful functors from the category of localic groups into any of the two categories of uniform locales. |
publishDate |
2011 |
dc.date.none.fl_str_mv |
2011 |
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/10316/43784 http://hdl.handle.net/10316/43784 https://doi.org/10.1007/s10485-011-9254-3 https://doi.org/10.1007/s10485-011-9254-3 |
url |
http://hdl.handle.net/10316/43784 https://doi.org/10.1007/s10485-011-9254-3 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://link.springer.com/article/10.1007%2Fs10485-011-9254-3 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Springer |
publisher.none.fl_str_mv |
Springer |
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 |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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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 |
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1799133821549936640 |