Some remarks on distributive semilattices

Autores
Celani, Sergio Arturo; Calomino, Ismael Maria
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we shall give a survey of the most important characterizations of the notion of distributivity in semilattices with greatest element and we will present some new through annihilators and relative maximal filters. We shall also simplify the topological representation for distributive semilattices given in cite{Celani} and show that the meet-relations are closed under composition. So, we obtain that the $DS$-spaces with meet-relations is a category dual to the category of distributive semilattices with homomorphisms. These results complete the topological representation presented in cite{Celani} without the use of ordered topological spaces. Finally, following the work of G. Bezhanishvili and R. Jansana in cite{Bezhanishvili-Jansana II}, we will prove a characterization of homomorphic images of a distributive semilattice $A$ by means of family of closed subsets of the dual space endowed with a lower Vitories topology.
Fil: Celani, Sergio Arturo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Tandil; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires; Argentina
Fil: Calomino, Ismael Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Tandil; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires; Argentina
Materia
Semilattices
Topological Representation
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:11336/7050
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/7050
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Some remarks on distributive semilatticesCelani, Sergio ArturoCalomino, Ismael MariaSemilatticesTopological Representationhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we shall give a survey of the most important characterizations of the notion of distributivity in semilattices with greatest element and we will present some new through annihilators and relative maximal filters. We shall also simplify the topological representation for distributive semilattices given in cite{Celani} and show that the meet-relations are closed under composition. So, we obtain that the $DS$-spaces with meet-relations is a category dual to the category of distributive semilattices with homomorphisms. These results complete the topological representation presented in cite{Celani} without the use of ordered topological spaces. Finally, following the work of G. Bezhanishvili and R. Jansana in cite{Bezhanishvili-Jansana II}, we will prove a characterization of homomorphic images of a distributive semilattice $A$ by means of family of closed subsets of the dual space endowed with a lower Vitories topology.Fil: Celani, Sergio Arturo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Tandil; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires; ArgentinaFil: Calomino, Ismael Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Tandil; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires; ArgentinaCharles University. Faculty of Mathematics and Physics2013-06info: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/11336/7050Celani, Sergio Arturo; Calomino, Ismael Maria; Some remarks on distributive semilattices; Charles University. Faculty of Mathematics and Physics; Commentationes Mathematicae; 54; 3; 6-2013; 407-4280010-2628enginfo:eu-repo/semantics/altIdentifier/url/https://cmuc.karlin.mff.cuni.cz/cmuc1303/abs/celani.htminfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:41:07Zoai:ri.conicet.gov.ar:11336/7050instacron: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:34982025-09-29 10:41:07.362CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Some remarks on distributive semilattices
title Some remarks on distributive semilattices
spellingShingle Some remarks on distributive semilattices
Celani, Sergio Arturo
Semilattices
Topological Representation
title_short Some remarks on distributive semilattices
title_full Some remarks on distributive semilattices
title_fullStr Some remarks on distributive semilattices
title_full_unstemmed Some remarks on distributive semilattices
title_sort Some remarks on distributive semilattices
dc.creator.none.fl_str_mv Celani, Sergio Arturo
Calomino, Ismael Maria
author Celani, Sergio Arturo
author_facet Celani, Sergio Arturo
Calomino, Ismael Maria
author_role author
author2 Calomino, Ismael Maria
author2_role author
dc.subject.none.fl_str_mv Semilattices
Topological Representation
topic Semilattices
Topological Representation
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 shall give a survey of the most important characterizations of the notion of distributivity in semilattices with greatest element and we will present some new through annihilators and relative maximal filters. We shall also simplify the topological representation for distributive semilattices given in cite{Celani} and show that the meet-relations are closed under composition. So, we obtain that the $DS$-spaces with meet-relations is a category dual to the category of distributive semilattices with homomorphisms. These results complete the topological representation presented in cite{Celani} without the use of ordered topological spaces. Finally, following the work of G. Bezhanishvili and R. Jansana in cite{Bezhanishvili-Jansana II}, we will prove a characterization of homomorphic images of a distributive semilattice $A$ by means of family of closed subsets of the dual space endowed with a lower Vitories topology.
Fil: Celani, Sergio Arturo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Tandil; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires; Argentina
Fil: Calomino, Ismael Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Tandil; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires; Argentina
description In this paper we shall give a survey of the most important characterizations of the notion of distributivity in semilattices with greatest element and we will present some new through annihilators and relative maximal filters. We shall also simplify the topological representation for distributive semilattices given in cite{Celani} and show that the meet-relations are closed under composition. So, we obtain that the $DS$-spaces with meet-relations is a category dual to the category of distributive semilattices with homomorphisms. These results complete the topological representation presented in cite{Celani} without the use of ordered topological spaces. Finally, following the work of G. Bezhanishvili and R. Jansana in cite{Bezhanishvili-Jansana II}, we will prove a characterization of homomorphic images of a distributive semilattice $A$ by means of family of closed subsets of the dual space endowed with a lower Vitories topology.
publishDate 2013
dc.date.none.fl_str_mv 2013-06
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/11336/7050
Celani, Sergio Arturo; Calomino, Ismael Maria; Some remarks on distributive semilattices; Charles University. Faculty of Mathematics and Physics; Commentationes Mathematicae; 54; 3; 6-2013; 407-428
0010-2628
url http://hdl.handle.net/11336/7050
identifier_str_mv Celani, Sergio Arturo; Calomino, Ismael Maria; Some remarks on distributive semilattices; Charles University. Faculty of Mathematics and Physics; Commentationes Mathematicae; 54; 3; 6-2013; 407-428
0010-2628
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://cmuc.karlin.mff.cuni.cz/cmuc1303/abs/celani.htm
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 Charles University. Faculty of Mathematics and Physics
publisher.none.fl_str_mv Charles University. Faculty of Mathematics and Physics
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 13.070432

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