Uniform-type structures on lattice-valued spaces and frames
Autor(a) principal: | |
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Data de Publicação: | 2008 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10316/4595 https://doi.org/10.1016/j.fss.2008.03.004 |
Resumo: | By introducing lattice-valued covers of a set, we present a general framework for uniform structures on very general L-valued spaces (for L an integral commutative quantale). By showing, via an intermediate L-valued structure of uniformity, how filters of covers may describe the uniform operators of Hutton, we prove that, when restricted to Girard quantales, this general framework captures a significant class of Hutton's uniform spaces. The categories ofL-valued uniform spaces and L-valued uniform frames here introduced provide (in the case L is a complete chain) the missing vertices in the commutative cube formed by the classical categories of topological and uniform spaces and their corresponding pointfree counterparts (forming the base of the cube) and the corresponding L-valued categories (forming the top of the cube). |
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7160 |
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Uniform-type structures on lattice-valued spaces and framesQuantaleGirard quantaleIntegral commutative quantaleL-valued spaceL-valued frameUniformityEntourageUniform operatorGalois connectionAxialityPolarityBy introducing lattice-valued covers of a set, we present a general framework for uniform structures on very general L-valued spaces (for L an integral commutative quantale). By showing, via an intermediate L-valued structure of uniformity, how filters of covers may describe the uniform operators of Hutton, we prove that, when restricted to Girard quantales, this general framework captures a significant class of Hutton's uniform spaces. The categories ofL-valued uniform spaces and L-valued uniform frames here introduced provide (in the case L is a complete chain) the missing vertices in the commutative cube formed by the classical categories of topological and uniform spaces and their corresponding pointfree counterparts (forming the base of the cube) and the corresponding L-valued categories (forming the top of the cube).http://www.sciencedirect.com/science/article/B6V05-4S21TH4-1/1/977fe355f240b1998e74eabadc8b61dd2008-09-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleaplication/PDFhttp://hdl.handle.net/10316/4595http://hdl.handle.net/10316/4595https://doi.org/10.1016/j.fss.2008.03.004engFuzzy Sets and Systems. In Press, Corrected Proof:Gutiérrez García, JavierMardones-Pérez, IraidePicado, JorgePrada Vicente, María Angeles deinfo: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:RCAAP2020-11-06T16:49:06Zoai:estudogeral.uc.pt:10316/4595Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:00:47.806075Repositório 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 |
Uniform-type structures on lattice-valued spaces and frames |
title |
Uniform-type structures on lattice-valued spaces and frames |
spellingShingle |
Uniform-type structures on lattice-valued spaces and frames Gutiérrez García, Javier Quantale Girard quantale Integral commutative quantale L-valued space L-valued frame Uniformity Entourage Uniform operator Galois connection Axiality Polarity |
title_short |
Uniform-type structures on lattice-valued spaces and frames |
title_full |
Uniform-type structures on lattice-valued spaces and frames |
title_fullStr |
Uniform-type structures on lattice-valued spaces and frames |
title_full_unstemmed |
Uniform-type structures on lattice-valued spaces and frames |
title_sort |
Uniform-type structures on lattice-valued spaces and frames |
author |
Gutiérrez García, Javier |
author_facet |
Gutiérrez García, Javier Mardones-Pérez, Iraide Picado, Jorge Prada Vicente, María Angeles de |
author_role |
author |
author2 |
Mardones-Pérez, Iraide Picado, Jorge Prada Vicente, María Angeles de |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Gutiérrez García, Javier Mardones-Pérez, Iraide Picado, Jorge Prada Vicente, María Angeles de |
dc.subject.por.fl_str_mv |
Quantale Girard quantale Integral commutative quantale L-valued space L-valued frame Uniformity Entourage Uniform operator Galois connection Axiality Polarity |
topic |
Quantale Girard quantale Integral commutative quantale L-valued space L-valued frame Uniformity Entourage Uniform operator Galois connection Axiality Polarity |
description |
By introducing lattice-valued covers of a set, we present a general framework for uniform structures on very general L-valued spaces (for L an integral commutative quantale). By showing, via an intermediate L-valued structure of uniformity, how filters of covers may describe the uniform operators of Hutton, we prove that, when restricted to Girard quantales, this general framework captures a significant class of Hutton's uniform spaces. The categories ofL-valued uniform spaces and L-valued uniform frames here introduced provide (in the case L is a complete chain) the missing vertices in the commutative cube formed by the classical categories of topological and uniform spaces and their corresponding pointfree counterparts (forming the base of the cube) and the corresponding L-valued categories (forming the top of the cube). |
publishDate |
2008 |
dc.date.none.fl_str_mv |
2008-09-01 |
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/10316/4595 http://hdl.handle.net/10316/4595 https://doi.org/10.1016/j.fss.2008.03.004 |
url |
http://hdl.handle.net/10316/4595 https://doi.org/10.1016/j.fss.2008.03.004 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Fuzzy Sets and Systems. In Press, Corrected Proof: |
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 |
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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) |
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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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1799133898413703168 |