Pointfree forms of Dowker and Michael insertion theorems

Bibliographic Details
Main Author: Gutiérrez García, Javier
Publication Date: 2007
Other Authors: Kubiak, Tomasz, Picado, Jorge
Format: Other
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: https://hdl.handle.net/10316/11276
Summary: In this paper we prove two strict insertion theorems for frame homomorphisms. When applied to the frame of all open subsets of a topological space they are equivalent to the insertion statements of the classical theorems of Dowker and Michael regarding, respectively, normal countably paracompact spaces and perfectly normal spaces. In addition, a study of perfect normality for frames is made.
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spelling Pointfree forms of Dowker and Michael insertion theoremsFrameSublocaleInsertion theoremExtension theoremKat¡etov relationContinuous real function on a frameLower semicontinuousUpper semicontinuousNormal framePerfectly normal frameCountably paracompact frameIn this paper we prove two strict insertion theorems for frame homomorphisms. When applied to the frame of all open subsets of a topological space they are equivalent to the insertion statements of the classical theorems of Dowker and Michael regarding, respectively, normal countably paracompact spaces and perfectly normal spaces. In addition, a study of perfect normality for frames is made.Ministry of Education and Science of Spain and FEDER under grant MTM2006-14925-C02-02. The third named author acknowledges financial support from the Centre of Mathematics of the University of Coimbra/FCT.Centro de Matemática da Universidade de Coimbra2007info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/otherhttps://hdl.handle.net/10316/11276https://hdl.handle.net/10316/11276engPré-Publicações DMUC. 07-41 (2007)Gutiérrez García, JavierKubiak, TomaszPicado, 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:RCAAP2020-05-25T13:10:49Zoai:estudogeral.uc.pt:10316/11276Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-29T05:23:19.737093Repositórios 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 Pointfree forms of Dowker and Michael insertion theorems
title Pointfree forms of Dowker and Michael insertion theorems
spellingShingle Pointfree forms of Dowker and Michael insertion theorems
Gutiérrez García, Javier
Frame
Sublocale
Insertion theorem
Extension theorem
Kat¡etov relation
Continuous real function on a frame
Lower semicontinuous
Upper semicontinuous
Normal frame
Perfectly normal frame
Countably paracompact frame
title_short Pointfree forms of Dowker and Michael insertion theorems
title_full Pointfree forms of Dowker and Michael insertion theorems
title_fullStr Pointfree forms of Dowker and Michael insertion theorems
title_full_unstemmed Pointfree forms of Dowker and Michael insertion theorems
title_sort Pointfree forms of Dowker and Michael insertion theorems
author Gutiérrez García, Javier
author_facet Gutiérrez García, Javier
Kubiak, Tomasz
Picado, Jorge
author_role author
author2 Kubiak, Tomasz
Picado, Jorge
author2_role author
author
dc.contributor.author.fl_str_mv Gutiérrez García, Javier
Kubiak, Tomasz
Picado, Jorge
dc.subject.por.fl_str_mv Frame
Sublocale
Insertion theorem
Extension theorem
Kat¡etov relation
Continuous real function on a frame
Lower semicontinuous
Upper semicontinuous
Normal frame
Perfectly normal frame
Countably paracompact frame
topic Frame
Sublocale
Insertion theorem
Extension theorem
Kat¡etov relation
Continuous real function on a frame
Lower semicontinuous
Upper semicontinuous
Normal frame
Perfectly normal frame
Countably paracompact frame
description In this paper we prove two strict insertion theorems for frame homomorphisms. When applied to the frame of all open subsets of a topological space they are equivalent to the insertion statements of the classical theorems of Dowker and Michael regarding, respectively, normal countably paracompact spaces and perfectly normal spaces. In addition, a study of perfect normality for frames is made.
publishDate 2007
dc.date.none.fl_str_mv 2007
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/other
format other
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://hdl.handle.net/10316/11276
https://hdl.handle.net/10316/11276
url https://hdl.handle.net/10316/11276
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Pré-Publicações DMUC. 07-41 (2007)
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Centro de Matemática da Universidade de Coimbra
publisher.none.fl_str_mv Centro de Matemática da Universidade de Coimbra
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_ 1833602338946809856

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