A strengthening of the Čech-Pospišil theorem
type: Item
instance of: scholarly article
title: A strengthening of the Čech-Pospišil theorem
zbMATH Open document ID: 1155.54007
author: István Juhász
author: Zoltán Szentmiklóssy
published in: Topology and its Applications
publication date: 2008-11-12T00:00:00Z
review text: For a space \(X\), dis\((X)\) denotes the smallest infinite cardinal \(\kappa\) such that \(X\) can be covered by \(\kappa\) discrete subspaces. A result is shown whose corollary is the following improvement of the famous Čech-Pospišil theorem [\textit{E. Čech} amd \textit{B. Pospišil}, Publ. Fac. Sci. Univ. Masaryk 258, 1--14 (1938; Zbl 0019.08903)]: if \(X\) is a compact Hausdorff space with \(\chi(x,X) \geq \kappa\) for each \(x\in X\), then dis\((X) \geq 2^{\kappa}\).
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54B05
zbMATH DE Number: 5365225
zbMATH Keywords: compact space
zbMATH Keywords: discrete subspace
zbMATH Keywords: \(dis(X)\)
zbMATH Keywords: covering
zbMATH Keywords: Čech-Pospišil theorem
reviewed by: Ljubiša D. R. Kočinac
MaRDI profile type: Publication
full work available at URL: j.topol.2007.04.021
OpenAlex ID: W2083351271
cites work: Q3938195
cites work: Covering compacta by discrete subspaces
DOI: 10.1016/J.TOPOL.2007.04.021
description: scientific article; zbMATH DE number 5365225