Countably QC-Approximating Posets

As a generalization of countably C-approximating posets, the concept of countably QC-approximating posets is introduced. With the countably QC-approximating property, some characterizations of generalized completely distributive lattices and generalized countably approximating posets are given. The...

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Detalles Bibliográficos
Autores principales: Mao, Xuxin, Xu, Luoshan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4138946/
https://www.ncbi.nlm.nih.gov/pubmed/25165730
http://dx.doi.org/10.1155/2014/123762
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author Mao, Xuxin
Xu, Luoshan
author_facet Mao, Xuxin
Xu, Luoshan
author_sort Mao, Xuxin
collection PubMed
description As a generalization of countably C-approximating posets, the concept of countably QC-approximating posets is introduced. With the countably QC-approximating property, some characterizations of generalized completely distributive lattices and generalized countably approximating posets are given. The main results are as follows: (1) a complete lattice is generalized completely distributive if and only if it is countably QC-approximating and weakly generalized countably approximating; (2) a poset L having countably directed joins is generalized countably approximating if and only if the lattice σ (c)(L)(op) of all σ-Scott-closed subsets of L is weakly generalized countably approximating.
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spelling pubmed-41389462014-08-27 Countably QC-Approximating Posets Mao, Xuxin Xu, Luoshan ScientificWorldJournal Research Article As a generalization of countably C-approximating posets, the concept of countably QC-approximating posets is introduced. With the countably QC-approximating property, some characterizations of generalized completely distributive lattices and generalized countably approximating posets are given. The main results are as follows: (1) a complete lattice is generalized completely distributive if and only if it is countably QC-approximating and weakly generalized countably approximating; (2) a poset L having countably directed joins is generalized countably approximating if and only if the lattice σ (c)(L)(op) of all σ-Scott-closed subsets of L is weakly generalized countably approximating. Hindawi Publishing Corporation 2014 2014-08-05 /pmc/articles/PMC4138946/ /pubmed/25165730 http://dx.doi.org/10.1155/2014/123762 Text en Copyright © 2014 X. Mao and L. Xu. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Mao, Xuxin
Xu, Luoshan
Countably QC-Approximating Posets
title Countably QC-Approximating Posets
title_full Countably QC-Approximating Posets
title_fullStr Countably QC-Approximating Posets
title_full_unstemmed Countably QC-Approximating Posets
title_short Countably QC-Approximating Posets
title_sort countably qc-approximating posets
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4138946/
https://www.ncbi.nlm.nih.gov/pubmed/25165730
http://dx.doi.org/10.1155/2014/123762
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