A new look at localic interpolation theorems
Autor(a) principal: | |
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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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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 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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1799133897138634752 |