The Priestley separation axiom for scattered spaces
type: Item
instance of: scholarly article
title: The Priestley separation axiom for scattered spaces
zbMATH Open document ID: 0995.54024
DOI: 10.1023/A:1015234920593
author: Guram Bezhanishvili
author: Ray Mines
author: Patrick Morandi
published in: Order
publication date: 2002-08-21T00:00:00Z
review text: The authors give a new characterization of scattered compact Hausdorff spaces. Main results: (1) Let \(X\) be a scattered compact Hausdorff space with a quasi-order \(R\). Then \(R\) is closed if and only if \((X,R)\) is a Priestley space. (2) Let \(X\) be a non-scattered compact Hausdorff space. Then there is a closed equivalence relation \(E\) on \(X\) such that \((X,E)\) is not a Priestley space. (3) Let \(X\) be a non-scattered compact Hausdorff metrizable space. Then there is a closed partial order \(\leq\) on \(X\) such that \((X,\leq)\) is not a Priestley space.
reviewed by: Bohumil František Šmarda
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 54G12
Mathematics Subject Classification ID: 06E15
zbMATH DE Number: 1785649
zbMATH Keywords: scattered space
zbMATH Keywords: Stone space
zbMATH Keywords: quasi-order
zbMATH Keywords: Priestley space
MaRDI profile type: Publication
full work available at URL: a:1015234920593
OpenAlex ID: W190083431
description: scientific article; zbMATH DE number 1785649