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On strong inclusions and asymmetric proximities in frames

Detalhes bibliográficos
Autor(a) principal: Picado, Jorge
Data de Publicação: 2010
Outros Autores: Pultr, Aleš
Tipo de documento: Outros
Idioma: eng
Título da fonte: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Texto Completo: https://hdl.handle.net/10316/13653
Resumo: The strong inclusion, a speci c type of subrelation of the order of a lattice with pseudocomplements, has been used in the concrete case of the lattice of open sets in topology for an expedient de nition of proximity, and allowed for a natural point-free extension of this concept. A modi cation of a strong inclusion for biframes then provided a point-free model also for the non-symmetric variant. In this paper we show that a strong inclusion can be non-symmetrically modi ed to work directly on frames, without prior assumption of a biframe structure. The category of quasi-proximal frames thus obtained is shown to be concretely isomorphic with the biframe based one, and shown to be related to that of quasi-uniform frames in a full analogy with the symmetric case.
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spelling On strong inclusions and asymmetric proximities in framesFrameBiframePseudocomplementStrong inclusionPaircoverQuasiuniform frameQuasi-proximal frameTotal boundednessThe strong inclusion, a speci c type of subrelation of the order of a lattice with pseudocomplements, has been used in the concrete case of the lattice of open sets in topology for an expedient de nition of proximity, and allowed for a natural point-free extension of this concept. A modi cation of a strong inclusion for biframes then provided a point-free model also for the non-symmetric variant. In this paper we show that a strong inclusion can be non-symmetrically modi ed to work directly on frames, without prior assumption of a biframe structure. The category of quasi-proximal frames thus obtained is shown to be concretely isomorphic with the biframe based one, and shown to be related to that of quasi-uniform frames in a full analogy with the symmetric case.Centro de Matemática da Universidade de Coimbra2010info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/otherhttps://hdl.handle.net/10316/13653https://hdl.handle.net/10316/13653engPré-Publicações DMUC. 10-25 (2010)Picado, JorgePultr, Alešinfo: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:RCAAP2020-01-22T12:05:42Zoai:estudogeral.uc.pt:10316/13653Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-29T05:23:25.076218Repositórios 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 On strong inclusions and asymmetric proximities in frames
title On strong inclusions and asymmetric proximities in frames
spellingShingle On strong inclusions and asymmetric proximities in frames
Picado, Jorge
Frame
Biframe
Pseudocomplement
Strong inclusion
Paircover
Quasiuniform frame
Quasi-proximal frame
Total boundedness
title_short On strong inclusions and asymmetric proximities in frames
title_full On strong inclusions and asymmetric proximities in frames
title_fullStr On strong inclusions and asymmetric proximities in frames
title_full_unstemmed On strong inclusions and asymmetric proximities in frames
title_sort On strong inclusions and asymmetric proximities in frames
author Picado, Jorge
author_facet Picado, Jorge
Pultr, Aleš
author_role author
author2 Pultr, Aleš
author2_role author
dc.contributor.author.fl_str_mv Picado, Jorge
Pultr, Aleš
dc.subject.por.fl_str_mv Frame
Biframe
Pseudocomplement
Strong inclusion
Paircover
Quasiuniform frame
Quasi-proximal frame
Total boundedness
topic Frame
Biframe
Pseudocomplement
Strong inclusion
Paircover
Quasiuniform frame
Quasi-proximal frame
Total boundedness
description The strong inclusion, a speci c type of subrelation of the order of a lattice with pseudocomplements, has been used in the concrete case of the lattice of open sets in topology for an expedient de nition of proximity, and allowed for a natural point-free extension of this concept. A modi cation of a strong inclusion for biframes then provided a point-free model also for the non-symmetric variant. In this paper we show that a strong inclusion can be non-symmetrically modi ed to work directly on frames, without prior assumption of a biframe structure. The category of quasi-proximal frames thus obtained is shown to be concretely isomorphic with the biframe based one, and shown to be related to that of quasi-uniform frames in a full analogy with the symmetric case.
publishDate 2010
dc.date.none.fl_str_mv 2010
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/10316/13653
https://hdl.handle.net/10316/13653
url https://hdl.handle.net/10316/13653
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Pré-Publicações DMUC. 10-25 (2010)
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
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