On the parallel between normality and extremal disconnectedness
Autor(a) principal: | |
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Data de Publicação: | 2014 |
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/10316/43789 https://doi.org/10.1016/j.jpaa.2013.10.002 |
Resumo: | Several familiar results about normal and extremally disconnected (classical or pointfree) spaces shape the idea that the two notions are somehow dual to each other and can therefore be studied in parallel. This paper investigates the source of this ‘duality’ and shows that each pair of parallel results can be framed by the ‘same’ proof. The key tools for this purpose are relative notions of normality, extremal disconnectedness, semicontinuity and continuity (with respect to a fixed class of complemented sublocales of the given locale) that bring and extend to locale theory a variety of well-known classical variants of normality and upper and lower semicontinuities in an illuminating unified manner. This approach allows us to unify under a single localic proof all classical insertion, as well as their corresponding extension results. |
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On the parallel between normality and extremal disconnectednessSeveral familiar results about normal and extremally disconnected (classical or pointfree) spaces shape the idea that the two notions are somehow dual to each other and can therefore be studied in parallel. This paper investigates the source of this ‘duality’ and shows that each pair of parallel results can be framed by the ‘same’ proof. The key tools for this purpose are relative notions of normality, extremal disconnectedness, semicontinuity and continuity (with respect to a fixed class of complemented sublocales of the given locale) that bring and extend to locale theory a variety of well-known classical variants of normality and upper and lower semicontinuities in an illuminating unified manner. This approach allows us to unify under a single localic proof all classical insertion, as well as their corresponding extension results.Elsevier2014info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/43789http://hdl.handle.net/10316/43789https://doi.org/10.1016/j.jpaa.2013.10.002https://doi.org/10.1016/j.jpaa.2013.10.002enghttp://www.sciencedirect.com/science/article/pii/S0022404913001771Gutiérrez García, JavierPicado, Jorgeinfo: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:RCAAP2021-06-29T10:03:02Zoai:estudogeral.uc.pt:10316/43789Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:27.556698Repositório 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 |
On the parallel between normality and extremal disconnectedness |
title |
On the parallel between normality and extremal disconnectedness |
spellingShingle |
On the parallel between normality and extremal disconnectedness Gutiérrez García, Javier |
title_short |
On the parallel between normality and extremal disconnectedness |
title_full |
On the parallel between normality and extremal disconnectedness |
title_fullStr |
On the parallel between normality and extremal disconnectedness |
title_full_unstemmed |
On the parallel between normality and extremal disconnectedness |
title_sort |
On the parallel between normality and extremal disconnectedness |
author |
Gutiérrez García, Javier |
author_facet |
Gutiérrez García, Javier Picado, Jorge |
author_role |
author |
author2 |
Picado, Jorge |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Gutiérrez García, Javier Picado, Jorge |
description |
Several familiar results about normal and extremally disconnected (classical or pointfree) spaces shape the idea that the two notions are somehow dual to each other and can therefore be studied in parallel. This paper investigates the source of this ‘duality’ and shows that each pair of parallel results can be framed by the ‘same’ proof. The key tools for this purpose are relative notions of normality, extremal disconnectedness, semicontinuity and continuity (with respect to a fixed class of complemented sublocales of the given locale) that bring and extend to locale theory a variety of well-known classical variants of normality and upper and lower semicontinuities in an illuminating unified manner. This approach allows us to unify under a single localic proof all classical insertion, as well as their corresponding extension results. |
publishDate |
2014 |
dc.date.none.fl_str_mv |
2014 |
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/10316/43789 http://hdl.handle.net/10316/43789 https://doi.org/10.1016/j.jpaa.2013.10.002 https://doi.org/10.1016/j.jpaa.2013.10.002 |
url |
http://hdl.handle.net/10316/43789 https://doi.org/10.1016/j.jpaa.2013.10.002 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
http://www.sciencedirect.com/science/article/pii/S0022404913001771 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
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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1799133821553082368 |