Regular spaces of small extent are \(\omega \)-resolvable
type: Item
instance of: scholarly article
zbMATH Open document ID: 1315.54005
author: István Juhász
author: Lajos Soukup
author: Zoltán Szentmiklóssy
published in: Fundamenta Mathematicae
publication date: 2014-11-07T00:00:00Z
full work available at URL: https://arxiv.org/abs/1311.1719
full work available at URL: 1311.1719v1.pdf
Mathematics Subject Classification ID: 54A35
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 03E35
zbMATH DE Number: 6366989
MaRDI profile type: Publication
OpenAlex ID: W2964042783
arXiv ID: 1311.1719
DOI: 10.4064/FM228-1-3
title: Regular spaces of small extent are \(\omega \)-resolvable
review text: Let \(X\) be a topological space. For a cardinal \(\lambda\), \(X\) is \(\lambda\)-resolvable if it contains \(\lambda\) many mutually disjoint dense subsets. The dispersion \(\Delta(X)\) of \(X\) is the minimum cardinality of non-empty open subsets of \(X\) while the extent e\((X)\) of \(X\) is the supremum of the cardinalities of closed discrete subsets of \(X\). It is shown that if \(X\) is regular with \(\Delta(X)>\text{e}(X)\) then \(X\) is \(\omega\)-resolvable. If, further, \(X\) is Lindelöf and \(|X|=\Delta(X)=\omega_1\) then \(X\) is \(\omega_1\)-resolvable.
reviewed by: David B. Gauld
description: scientific article; zbMATH DE number 6366989