Strongly zero-dimensional locales
type: Item
instance of: scholarly article
title: Strongly zero-dimensional locales
zbMATH Open document ID: 0996.06006
author: Hui Kou
author: Maokang Luo
publication date: 2002-11-04T00:00:00Z
review text: The authors introduce a new definition of strongly zero-dimensional locales. Their conception is different from Johnstone's and almost all topological properties for strongly zero-dimensional spaces have a pointless localic form. Some properties and characterizations: (1) A topological space \(X\) is strongly zero-dimensional iff the lattice \(O(X)\) of open sets is strongly zero-dimensional. (2) A strongly zero-dimensional locale is zero-dimensional. A zero-dimensional Lindelöf locale is a strongly zero-dimensional locale. (3) For a compact locale, strong zero-dimensionality, zero-dimensionality and strong zero-dimensionality in Johnstone's sense are equivalent to each other. (4) The Stone-Čech compactification of a strongly zero-dimensional locale is strongly zero-dimensional.
reviewed by: Bohumil František Šmarda
Mathematics Subject Classification ID: 06D22
Mathematics Subject Classification ID: 54A05
Mathematics Subject Classification ID: 54D30
zbMATH DE Number: 1757445
zbMATH Keywords: strongly zero-dimensional locales
zbMATH Keywords: Stone-Čech compactification
MaRDI profile type: Publication
full work available at URL: s101140000072
OpenAlex ID: W2044462345
cites work: Cartesian monads on toposes
cites work: Alexandroff Algebras and Complete Regularity
cites work: Realcompact spaces and regular σ -frames
cites work: Q4374682
cites work: Q3153986
DOI: 10.1007/S101140000072
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 1757445