Remarks on Priestley duality for distributive lattices

The notion of a Priestley relation between Priestley spaces is introduced, and it is shown that there is a duality between the category of bounded distributive lattices and 0-preserving join-homomorphisms and the category of Priestley spaces and Priestley relations. When restricted to the category o...

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Autor principal:	Petrovich, Alejandro Gustavo
Publicado:	1991
Materias:	AMS subject classification (1991): 06D05 Bounded distributive lattices closure operators filters ideals lattice homomorphisms Priestley spaces quantifiers sublattices
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01678094_v8_n3_p299_Cignoli http://hdl.handle.net/20.500.12110/paper_01678094_v8_n3_p299_Cignoli
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_01678094_v8_n3_p299_Cignoli
record_format	dspace
spelling	paper:paper_01678094_v8_n3_p299_Cignoli2023-06-08T15:16:58Z Remarks on Priestley duality for distributive lattices Petrovich, Alejandro Gustavo AMS subject classification (1991): 06D05 Bounded distributive lattices closure operators filters ideals lattice homomorphisms Priestley spaces quantifiers sublattices The notion of a Priestley relation between Priestley spaces is introduced, and it is shown that there is a duality between the category of bounded distributive lattices and 0-preserving join-homomorphisms and the category of Priestley spaces and Priestley relations. When restricted to the category of bounded distributive lattices and 0-1-preserving homomorphisms, this duality yields essentially Priestley duality, and when restricted to the subcategory of Boolean algebras and 0-preserving join-homomorphisms, it coincides with the Halmos-Wright duality. It is also established a duality between 0-1-sublattices of a bounded distributive lattice and certain preorder relations on its Priestley space, which are called lattice preorders. This duality is a natural generalization of the Boolean case, and is strongly related to one considered by M. E. Adams. Connections between both kinds of dualities are studied, obtaining dualities for closure operators and quantifiers. Some results on the existence of homomorphisms lying between meet and join homomorphisms are given in the Appendix. © 1991 Kluwer Academic Publishers. Fil:Petrovich, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 1991 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01678094_v8_n3_p299_Cignoli http://hdl.handle.net/20.500.12110/paper_01678094_v8_n3_p299_Cignoli
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	AMS subject classification (1991): 06D05 Bounded distributive lattices closure operators filters ideals lattice homomorphisms Priestley spaces quantifiers sublattices
spellingShingle	AMS subject classification (1991): 06D05 Bounded distributive lattices closure operators filters ideals lattice homomorphisms Priestley spaces quantifiers sublattices Petrovich, Alejandro Gustavo Remarks on Priestley duality for distributive lattices
topic_facet	AMS subject classification (1991): 06D05 Bounded distributive lattices closure operators filters ideals lattice homomorphisms Priestley spaces quantifiers sublattices
description	The notion of a Priestley relation between Priestley spaces is introduced, and it is shown that there is a duality between the category of bounded distributive lattices and 0-preserving join-homomorphisms and the category of Priestley spaces and Priestley relations. When restricted to the category of bounded distributive lattices and 0-1-preserving homomorphisms, this duality yields essentially Priestley duality, and when restricted to the subcategory of Boolean algebras and 0-preserving join-homomorphisms, it coincides with the Halmos-Wright duality. It is also established a duality between 0-1-sublattices of a bounded distributive lattice and certain preorder relations on its Priestley space, which are called lattice preorders. This duality is a natural generalization of the Boolean case, and is strongly related to one considered by M. E. Adams. Connections between both kinds of dualities are studied, obtaining dualities for closure operators and quantifiers. Some results on the existence of homomorphisms lying between meet and join homomorphisms are given in the Appendix. © 1991 Kluwer Academic Publishers.
author	Petrovich, Alejandro Gustavo
author_facet	Petrovich, Alejandro Gustavo
author_sort	Petrovich, Alejandro Gustavo
title	Remarks on Priestley duality for distributive lattices
title_short	Remarks on Priestley duality for distributive lattices
title_full	Remarks on Priestley duality for distributive lattices
title_fullStr	Remarks on Priestley duality for distributive lattices
title_full_unstemmed	Remarks on Priestley duality for distributive lattices
title_sort	remarks on priestley duality for distributive lattices
publishDate	1991
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01678094_v8_n3_p299_Cignoli http://hdl.handle.net/20.500.12110/paper_01678094_v8_n3_p299_Cignoli
work_keys_str_mv	AT petrovichalejandrogustavo remarksonpriestleydualityfordistributivelattices
_version_	1768545968726212608

Remarks on Priestley duality for distributive lattices

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