Localic maps constructed from open and closed parts
Autor(a) principal: | |
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Data de Publicação: | 2017 |
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/10316/43954 |
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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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 |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10316/43954 http://hdl.handle.net/10316/43954 |
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 |
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 |
|
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1799133821634871296 |