Convergence in [Formula: see text] -quasicontinuous posets

In this paper, we present one way to generalize [Formula: see text] -convergence and [Formula: see text] -convergence of nets for arbitrary posets by use of the cut operator instead of joins. Some convergence theoretical characterizations of [Formula: see text] -continuity and [Formula: see text] -q...

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Autores principales: Ruan, Xiao-jun, Xu, Xiao-quan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2016
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4771692/
https://www.ncbi.nlm.nih.gov/pubmed/27026912
http://dx.doi.org/10.1186/s40064-016-1873-6
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author Ruan, Xiao-jun
Xu, Xiao-quan
author_facet Ruan, Xiao-jun
Xu, Xiao-quan
author_sort Ruan, Xiao-jun
collection PubMed
description In this paper, we present one way to generalize [Formula: see text] -convergence and [Formula: see text] -convergence of nets for arbitrary posets by use of the cut operator instead of joins. Some convergence theoretical characterizations of [Formula: see text] -continuity and [Formula: see text] -quasicontinuity of posets are given. The main results are: (1) a poset P is [Formula: see text] -continuous if and only if the [Formula: see text] -convergence in P is topological; (2) P is [Formula: see text] -quasicontinuous if and only if the [Formula: see text] -convergence in P is topological.
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spelling pubmed-47716922016-03-29 Convergence in [Formula: see text] -quasicontinuous posets Ruan, Xiao-jun Xu, Xiao-quan Springerplus Research In this paper, we present one way to generalize [Formula: see text] -convergence and [Formula: see text] -convergence of nets for arbitrary posets by use of the cut operator instead of joins. Some convergence theoretical characterizations of [Formula: see text] -continuity and [Formula: see text] -quasicontinuity of posets are given. The main results are: (1) a poset P is [Formula: see text] -continuous if and only if the [Formula: see text] -convergence in P is topological; (2) P is [Formula: see text] -quasicontinuous if and only if the [Formula: see text] -convergence in P is topological. Springer International Publishing 2016-02-29 /pmc/articles/PMC4771692/ /pubmed/27026912 http://dx.doi.org/10.1186/s40064-016-1873-6 Text en © Ruan and Xu. 2016 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Ruan, Xiao-jun
Xu, Xiao-quan
Convergence in [Formula: see text] -quasicontinuous posets
title Convergence in [Formula: see text] -quasicontinuous posets
title_full Convergence in [Formula: see text] -quasicontinuous posets
title_fullStr Convergence in [Formula: see text] -quasicontinuous posets
title_full_unstemmed Convergence in [Formula: see text] -quasicontinuous posets
title_short Convergence in [Formula: see text] -quasicontinuous posets
title_sort convergence in [formula: see text] -quasicontinuous posets
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4771692/
https://www.ncbi.nlm.nih.gov/pubmed/27026912
http://dx.doi.org/10.1186/s40064-016-1873-6
work_keys_str_mv AT ruanxiaojun convergenceinformulaseetextquasicontinuousposets
AT xuxiaoquan convergenceinformulaseetextquasicontinuousposets

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