A discussion of well-filteredness and sobriety
type: Item
instance of: scholarly article
title: A discussion of well-filteredness and sobriety
zbMATH Open document ID: 1462.54024
author: Hualin Miao
author: Zhenzhu Yuan
author: Qingguo Li
published in: Topology and its Applications
publication date: 2021-03-09T00:00:00Z
review text: The authors work in the framework of directed complete partially ordered sets, and items related to the notion of soberness. In this paper, they give a sufficient condition for a core-compact dcpo to be sober. Then they introduce and study a new kind of posets, namely the so-called join continuous posets. Also, they settle and analyze several relationships arising among sober, well-filtered and weak well-filtered topological properties. Based on the results they get, some characterizations for a poset to be Lawson compact are achieved. Moreover, they solve some open questions issued in this literature, posed by \textit{X. Xu} and \textit{D. Zhao} [Topology Appl. 272, Article ID 107080, 14 p. (2020; Zbl 1477.06020)].
Mathematics Subject Classification ID: 54D99
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 06B35
Mathematics Subject Classification ID: 06F30
Mathematics Subject Classification ID: 54A20
zbMATH DE Number: 7318660
zbMATH Keywords: sober
zbMATH Keywords: well-filtered dcpo
zbMATH Keywords: Lawson compactness
zbMATH Keywords: core-compact
reviewed by: Esteban Induraín
MaRDI profile type: Publication
full work available at URL: j.topol.2020.107450
OpenAlex ID: W3106560406
cites work: Non-Hausdorff Topology and Domain Theory
cites work: Continuous Lattices and Domains
cites work: A note on coherence of dcpos
cites work: Weak well-filtered spaces and coherence
cites work: Q4965631
cites work: On well-filtered reflections of \(T_0\) spaces
cites work: On well-filtered spaces and ordered sets
cites work: On topological Rudin's lemma, well-filtered spaces and sober spaces
cites work: Completion of a Construction of Johnstone
DOI: 10.1016/J.TOPOL.2020.107450
description: scientific article; zbMATH DE number 7318660