A new look at localic interpolation theorems

Bibliographic Details
Main Author: Picado, Jorge
Publication Date: 2006
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: https://hdl.handle.net/10316/4615
https://doi.org/10.1016/j.topol.2004.10.022
Summary: 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.
id RCAP_5d3d35a939ea9a51465e63c893d32cd6
oai_identifier_str oai:estudogeral.uc.pt:10316/4615
network_acronym_str RCAP
network_name_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository_id_str https://opendoar.ac.uk/repository/7160
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/PDFhttps://hdl.handle.net/10316/4615https://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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2020-11-06T16:59:23Zoai:estudogeral.uc.pt:10316/4615Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-29T05:23:12.779379Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
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 https://hdl.handle.net/10316/4615
https://hdl.handle.net/10316/4615
https://doi.org/10.1016/j.topol.2004.10.022
url https://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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
_version_ 1833602338222243840

Similar Items