A new look at localic interpolation theorems

Detalhes bibliográficos
Autor(a) principal: Picado, Jorge
Data de Publicação: 2006
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10316/4615
https://doi.org/10.1016/j.topol.2004.10.022
Resumo: This paper presents a new treatment of the localic Katetov-Tong interpolation theorem, based on an analysis of special properties of normal frames, which shows that it does not hold in full generality. Besides giving us the conditions under which the localic Katetov-Tong interpolation theorem holds, this approach leads to a especially transparent and succinct proof of it. It is also shown that this pointfree extension of Katetov-Tong theorem still covers the localic versions of Urysohn's Lemma and Tietze's Extension Theorem.
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spelling A new look at localic interpolation theoremsLocalesNormal framesFrame of realsUpper (lower) frame of realsContinuous real functionsUpper (lower) semicontinuous real functionsThis paper presents a new treatment of the localic Katetov-Tong interpolation theorem, based on an analysis of special properties of normal frames, which shows that it does not hold in full generality. Besides giving us the conditions under which the localic Katetov-Tong interpolation theorem holds, this approach leads to a especially transparent and succinct proof of it. It is also shown that this pointfree extension of Katetov-Tong theorem still covers the localic versions of Urysohn's Lemma and Tietze's Extension Theorem.http://www.sciencedirect.com/science/article/B6V1K-4GWBDP0-3/1/c51690ad60d2e54badeac9b463852c5e2006info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleaplication/PDFhttp://hdl.handle.net/10316/4615http://hdl.handle.net/10316/4615https://doi.org/10.1016/j.topol.2004.10.022engTopology and its Applications. 153:16 (2006) 3203-3218Picado, 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:RCAAP2020-11-06T16:59:23Zoai:estudogeral.uc.pt:10316/4615Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:00:41.697876Repositório 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 A new look at localic interpolation theorems
title A new look at localic interpolation theorems
spellingShingle A new look at localic interpolation theorems
Picado, Jorge
Locales
Normal frames
Frame of reals
Upper (lower) frame of reals
Continuous real functions
Upper (lower) semicontinuous real functions
title_short A new look at localic interpolation theorems
title_full A new look at localic interpolation theorems
title_fullStr A new look at localic interpolation theorems
title_full_unstemmed A new look at localic interpolation theorems
title_sort A new look at localic interpolation theorems
author Picado, Jorge
author_facet Picado, Jorge
author_role author
dc.contributor.author.fl_str_mv Picado, Jorge
dc.subject.por.fl_str_mv Locales
Normal frames
Frame of reals
Upper (lower) frame of reals
Continuous real functions
Upper (lower) semicontinuous real functions
topic Locales
Normal frames
Frame of reals
Upper (lower) frame of reals
Continuous real functions
Upper (lower) semicontinuous real functions
description This paper presents a new treatment of the localic Katetov-Tong interpolation theorem, based on an analysis of special properties of normal frames, which shows that it does not hold in full generality. Besides giving us the conditions under which the localic Katetov-Tong interpolation theorem holds, this approach leads to a especially transparent and succinct proof of it. It is also shown that this pointfree extension of Katetov-Tong theorem still covers the localic versions of Urysohn's Lemma and Tietze's Extension Theorem.
publishDate 2006
dc.date.none.fl_str_mv 2006
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/10316/4615
http://hdl.handle.net/10316/4615
https://doi.org/10.1016/j.topol.2004.10.022
url http://hdl.handle.net/10316/4615
https://doi.org/10.1016/j.topol.2004.10.022
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Topology and its Applications. 153:16 (2006) 3203-3218
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv aplication/PDF
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
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instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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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
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