Resolvability of Lindelöf spaces
type: Item
instance of: scholarly article
title: Resolvability of Lindelöf spaces
zbMATH Open document ID: 1172.54015
author: M. A. Filatova
published in: Journal of Mathematical Sciences (New York)
publication date: 2008-10-28T00:00:00Z
review text: A topological space \(X\) is called \(\lambda\)-resolvable if it can be represented as the union of \(\lambda\) dense disjoint subsets; 2-resolvable spaces are called simply resolvable. A cardinal number \(\Delta(X)\) is said to be a dispersion character of a space \(X\) if \(\Delta(X)=\min\{|U|:U \text{ open subset of} X\}\). In the paper under review it is proved that every regular Lindelöf space of uncountable dispersion character is resolvable. This is an affirmative answer to a question posed by \textit{V. I. Malykhin} [Math. Notes 64, No.~5, 607--615 (1998); translation from Mat. Zametki 64, No.~5, 701--712 (1998; Zbl 0936.54039)]. Another result is that a hereditarily finally compact space of uncountable dispersion character is \(\omega\)-resolvable. A topological space is called finally compact if any open cover of \(X\) has a countable subcover.
reviewed by: Andrzej Kucharski
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54D10
zbMATH DE Number: 5358107
zbMATH Keywords: Lindelöf space
zbMATH Keywords: resolvable space
MaRDI profile type: Publication
full work available at URL: s10958-007-0373-1
OpenAlex ID: W2047115994
cites work: Resolvability: A selective survey and some new results
cites work: A problem of set-theoretic topology
cites work: Borel resolvability of compact spaces and their subspaces
cites work: Maximal resolvability of bounded groups
cites work: On resolvability of topological spaces
DOI: 10.1007/S10958-007-0373-1
description: scientific article; zbMATH DE number 5358107