Axiom TD and the Simmons sublocale theorem
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/10316/90469 https://doi.org/10.14712/1213-7243.2019.030 |
Resumo: | More precisely, we are analyzing some of H. Simmons, S. B. Niefield and K. I. Rosenthal results concerning sublocales induced by subspaces. H. Simmons was concerned with the question when the coframe of sublocales is Boolean; he recognized the role of the axiom $T_D$ for the relation of certain degrees of scatteredness but did not emphasize its role in the relation {between} sublocales and subspaces. S. B. Niefield and K. I. Rosenthal just mention this axiom in a remark about Simmons' result. In this paper we show that the role of $T_D$ in this question is crucial. Concentration on the properties of $T_D$-spaces and technique of sublocales in this context allows us to present a simple, transparent and choice-free proof of the scatteredness theorem. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Axiom TD and the Simmons sublocale theoremFrame; locale; sublocale; coframe of sublocales; spatial sublocale; induced sublocale; $T_D$-separation; covered prime element; scattered space; weakly scattered space.More precisely, we are analyzing some of H. Simmons, S. B. Niefield and K. I. Rosenthal results concerning sublocales induced by subspaces. H. Simmons was concerned with the question when the coframe of sublocales is Boolean; he recognized the role of the axiom $T_D$ for the relation of certain degrees of scatteredness but did not emphasize its role in the relation {between} sublocales and subspaces. S. B. Niefield and K. I. Rosenthal just mention this axiom in a remark about Simmons' result. In this paper we show that the role of $T_D$ in this question is crucial. Concentration on the properties of $T_D$-spaces and technique of sublocales in this context allows us to present a simple, transparent and choice-free proof of the scatteredness theorem.Mathematical Institute of Charles University2019info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/90469http://hdl.handle.net/10316/90469https://doi.org/10.14712/1213-7243.2019.030enghttps://cmuc.karlin.mff.cuni.cz/cmuc1904/abs/picpul.htmPicado, 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:RCAAP2022-05-25T03:12:30Zoai:estudogeral.uc.pt:10316/90469Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:10:35.992016Repositório 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 |
Axiom TD and the Simmons sublocale theorem |
title |
Axiom TD and the Simmons sublocale theorem |
spellingShingle |
Axiom TD and the Simmons sublocale theorem Picado, Jorge Frame; locale; sublocale; coframe of sublocales; spatial sublocale; induced sublocale; $T_D$-separation; covered prime element; scattered space; weakly scattered space. |
title_short |
Axiom TD and the Simmons sublocale theorem |
title_full |
Axiom TD and the Simmons sublocale theorem |
title_fullStr |
Axiom TD and the Simmons sublocale theorem |
title_full_unstemmed |
Axiom TD and the Simmons sublocale theorem |
title_sort |
Axiom TD and the Simmons sublocale theorem |
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 |
dc.subject.por.fl_str_mv |
Frame; locale; sublocale; coframe of sublocales; spatial sublocale; induced sublocale; $T_D$-separation; covered prime element; scattered space; weakly scattered space. |
topic |
Frame; locale; sublocale; coframe of sublocales; spatial sublocale; induced sublocale; $T_D$-separation; covered prime element; scattered space; weakly scattered space. |
description |
More precisely, we are analyzing some of H. Simmons, S. B. Niefield and K. I. Rosenthal results concerning sublocales induced by subspaces. H. Simmons was concerned with the question when the coframe of sublocales is Boolean; he recognized the role of the axiom $T_D$ for the relation of certain degrees of scatteredness but did not emphasize its role in the relation {between} sublocales and subspaces. S. B. Niefield and K. I. Rosenthal just mention this axiom in a remark about Simmons' result. In this paper we show that the role of $T_D$ in this question is crucial. Concentration on the properties of $T_D$-spaces and technique of sublocales in this context allows us to present a simple, transparent and choice-free proof of the scatteredness theorem. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019 |
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/10316/90469 http://hdl.handle.net/10316/90469 https://doi.org/10.14712/1213-7243.2019.030 |
url |
http://hdl.handle.net/10316/90469 https://doi.org/10.14712/1213-7243.2019.030 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://cmuc.karlin.mff.cuni.cz/cmuc1904/abs/picpul.htm |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Mathematical Institute of Charles University |
publisher.none.fl_str_mv |
Mathematical Institute of Charles 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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1799134000386670592 |