Topological representation for implication algebras

Autores
Abad, Manuel; Díaz Varela, José Patricio; Torrens, Antoni
Año de publicación
2004
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we give a description of an implication algebra A as a union of a unique family of filters of a suitable Boolean algebra Bo(A), called the Boolean closure of A. From this representation we obtain a notion of topological implication space and we give a dual equivalence based in the Stone representation for Boolean algebras. As an application we provide the implication space of all free implication algebras.
Fil: Abad, Manuel. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Fil: Díaz Varela, José Patricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Fil: Torrens, Antoni. Universidad de Barcelona; España
Materia
BOOLEAN ALGEBRAS
BOOLEAN SPACES
DUAL CATEGORICAL EQUIVALENCE
IMPLICATION ALGEBRAS
IMPLICATION SPACES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/95363
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/95363
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Topological representation for implication algebrasAbad, ManuelDíaz Varela, José PatricioTorrens, AntoniBOOLEAN ALGEBRASBOOLEAN SPACESDUAL CATEGORICAL EQUIVALENCEIMPLICATION ALGEBRASIMPLICATION SPACEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we give a description of an implication algebra A as a union of a unique family of filters of a suitable Boolean algebra Bo(A), called the Boolean closure of A. From this representation we obtain a notion of topological implication space and we give a dual equivalence based in the Stone representation for Boolean algebras. As an application we provide the implication space of all free implication algebras.Fil: Abad, Manuel. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaFil: Díaz Varela, José Patricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Torrens, Antoni. Universidad de Barcelona; EspañaBirkhauser Verlag Ag2004-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/95363Abad, Manuel; Díaz Varela, José Patricio; Torrens, Antoni; Topological representation for implication algebras; Birkhauser Verlag Ag; Algebra Universalis; 52; 1; 11-2004; 39-480002-5240CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00012-004-1872-2info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00012-004-1872-2#article-infoinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:13:04Zoai:ri.conicet.gov.ar:11336/95363instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:13:05.088CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Topological representation for implication algebras
title Topological representation for implication algebras
spellingShingle Topological representation for implication algebras
Abad, Manuel
BOOLEAN ALGEBRAS
BOOLEAN SPACES
DUAL CATEGORICAL EQUIVALENCE
IMPLICATION ALGEBRAS
IMPLICATION SPACES
title_short Topological representation for implication algebras
title_full Topological representation for implication algebras
title_fullStr Topological representation for implication algebras
title_full_unstemmed Topological representation for implication algebras
title_sort Topological representation for implication algebras
dc.creator.none.fl_str_mv Abad, Manuel
Díaz Varela, José Patricio
Torrens, Antoni
author Abad, Manuel
author_facet Abad, Manuel
Díaz Varela, José Patricio
Torrens, Antoni
author_role author
author2 Díaz Varela, José Patricio
Torrens, Antoni
author2_role author
author
dc.subject.none.fl_str_mv BOOLEAN ALGEBRAS
BOOLEAN SPACES
DUAL CATEGORICAL EQUIVALENCE
IMPLICATION ALGEBRAS
IMPLICATION SPACES
topic BOOLEAN ALGEBRAS
BOOLEAN SPACES
DUAL CATEGORICAL EQUIVALENCE
IMPLICATION ALGEBRAS
IMPLICATION SPACES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper we give a description of an implication algebra A as a union of a unique family of filters of a suitable Boolean algebra Bo(A), called the Boolean closure of A. From this representation we obtain a notion of topological implication space and we give a dual equivalence based in the Stone representation for Boolean algebras. As an application we provide the implication space of all free implication algebras.
Fil: Abad, Manuel. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Fil: Díaz Varela, José Patricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Fil: Torrens, Antoni. Universidad de Barcelona; España
description In this paper we give a description of an implication algebra A as a union of a unique family of filters of a suitable Boolean algebra Bo(A), called the Boolean closure of A. From this representation we obtain a notion of topological implication space and we give a dual equivalence based in the Stone representation for Boolean algebras. As an application we provide the implication space of all free implication algebras.
publishDate 2004
dc.date.none.fl_str_mv 2004-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/95363
Abad, Manuel; Díaz Varela, José Patricio; Torrens, Antoni; Topological representation for implication algebras; Birkhauser Verlag Ag; Algebra Universalis; 52; 1; 11-2004; 39-48
0002-5240
CONICET Digital
CONICET
url http://hdl.handle.net/11336/95363
identifier_str_mv Abad, Manuel; Díaz Varela, José Patricio; Torrens, Antoni; Topological representation for implication algebras; Birkhauser Verlag Ag; Algebra Universalis; 52; 1; 11-2004; 39-48
0002-5240
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00012-004-1872-2
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00012-004-1872-2#article-info
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Birkhauser Verlag Ag
publisher.none.fl_str_mv Birkhauser Verlag Ag
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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