Compactifications of quasi-uniform hyperspaces.
type: Item
instance of: scholarly article
title: Compactifications of quasi-uniform hyperspaces.
zbMATH Open document ID: 1033.54012
DOI: 10.1016/S0166-8641(02)00102-5
published in: Topology and its Applications
publication date: 2003-04-28T00:00:00Z
review text: In this paper the authors study compactifications of quasi-uniform hyperspaces. They prove among other things that for a Tychonoff space \(X\), the hyperspace \(2^{\beta X}\) is equivalent to the \({}^*\)-compactification of \(({\mathcal C}_0(X), {\mathcal P}{\mathcal N}_H)\) if and only if \(X\) is normal. From this they deduce that if \(X\) is normal and Hausdorff then \(\beta 2^X\) is equivalent to the \({}^*\)-compactification of \(({\mathcal C}_0(X), {\mathcal P}{\mathcal N}_H)\) if and only if \(2^X\) is pseudocompact.
reviewed by: Jan van Mill
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 54B20
zbMATH DE Number: 1901914
zbMATH Keywords: \(*\)-compactification
zbMATH Keywords: Vietoris topology
zbMATH Keywords: Bourbaki quasi-uniformity
author: Salvador Romaguera
author: Miguel Angel Sanchez Granero
MaRDI profile type: Publication
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full work available at URL: s0166-8641(02)00102-5
OpenAlex ID: W2036429387
description: scientific article; zbMATH DE number 1901914