Localic maps constructed from open and closed parts

Detalhes bibliográficos
Autor(a) principal: Picado, Jorge
Data de Publicação: 2017
Outros Autores: Pultr, Aleš
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10316/43954
Resumo: Assembling a localic map f:L→M from localic maps f_i:S_i→M, i∈J, defined on closed resp. open sublocales (J finite in the closed case) follows the same rules as in the classical case. The corresponding classical facts immediately follow from the behavior of preimages but for obvious reasons such a proof cannot be imitated in the point-free context. Instead, we present simple proofs based on categorical reasoning. There are some related aspects of localic preimages that are of interest, though. They are investigated in the second half of the paper.
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spelling Localic maps constructed from open and closed partsAssembling a localic map f:L→M from localic maps f_i:S_i→M, i∈J, defined on closed resp. open sublocales (J finite in the closed case) follows the same rules as in the classical case. The corresponding classical facts immediately follow from the behavior of preimages but for obvious reasons such a proof cannot be imitated in the point-free context. Instead, we present simple proofs based on categorical reasoning. There are some related aspects of localic preimages that are of interest, though. They are investigated in the second half of the paper.Shahid Beheshti University2017info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/43954http://hdl.handle.net/10316/43954enghttp://www.cgasa.ir/article_15806.htmlPicado, 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:RCAAP2020-01-22T12:05:41Zoai:estudogeral.uc.pt:10316/43954Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:30.819727Repositório 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 Localic maps constructed from open and closed parts
title Localic maps constructed from open and closed parts
spellingShingle Localic maps constructed from open and closed parts
Picado, Jorge
title_short Localic maps constructed from open and closed parts
title_full Localic maps constructed from open and closed parts
title_fullStr Localic maps constructed from open and closed parts
title_full_unstemmed Localic maps constructed from open and closed parts
title_sort Localic maps constructed from open and closed parts
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 Assembling a localic map f:L→M from localic maps f_i:S_i→M, i∈J, defined on closed resp. open sublocales (J finite in the closed case) follows the same rules as in the classical case. The corresponding classical facts immediately follow from the behavior of preimages but for obvious reasons such a proof cannot be imitated in the point-free context. Instead, we present simple proofs based on categorical reasoning. There are some related aspects of localic preimages that are of interest, though. They are investigated in the second half of the paper.
publishDate 2017
dc.date.none.fl_str_mv 2017
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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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10316/43954
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url http://hdl.handle.net/10316/43954
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv http://www.cgasa.ir/article_15806.html
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Shahid Beheshti University
publisher.none.fl_str_mv Shahid Beheshti University
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
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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
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