Stone-Čech remainders of nowhere locally compact spaces
type: Item
instance of: scholarly article
title: Stone-Čech remainders of nowhere locally compact spaces
zbMATH Open document ID: 1199.54154
author: James Hatzenbuhler
author: Don A. Mattson
published in: Acta Mathematica Hungarica
publication date: 2009-12-29T00:00:00Z
review text: All topological spaces are completely regular and Hausdorff, and we suppose that \(X\) is a nowhere locally compact space. The authors show that, for every compactification \(\alpha X\) of \(X\) such that the space \(\alpha X-X\) is extremally disconnected, we have \(\alpha X=\beta X\), where \(\beta X\) is the Čech-Stone compactification of \(X\). Furthermore, equivalent conditions are given for the space \(\beta X-X\) to be extremally disconnected. These results extend those of \textit{E. K. van Douwen} [Topology Appl. 47, No.~3, 165--171 (1992; Zbl 0766.54024)]. In conclusion, a characterization of the property \(\beta X-X\) being 0-dimensional by means of free \(z\)-ultrafilters in \(X\) is presented.
reviewed by: Ladislav Skula
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 54D40
zbMATH DE Number: 5651927
zbMATH Keywords: nowhere locally compact spaces
zbMATH Keywords: \(\beta X-X\) extremally disconnected
zbMATH Keywords: \(\beta X-X\) zero-dimensional
zbMATH Keywords: remainder
zbMATH Keywords: Čech-Stone compactification
MaRDI profile type: Publication
full work available at URL: s10474-009-7154-x
OpenAlex ID: W2080356295
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DOI: 10.1007/S10474-009-7154-X
description: scientific article; zbMATH DE number 5651927