\(\varepsilon\)-spaces
type: Item
instance of: scholarly article
title: \(\varepsilon\)-spaces
zbMATH Open document ID: 0849.54018
author: Richard N. Ball
author: Anthony W. Hager
author: Jan van Mill
author: Lewis C. Robertson
author: W. W. Comfort
author: Salvador Garcia-Ferreira
published in: Rocky Mountain Journal of Mathematics
publication date: 1996-11-11T00:00:00Z
review text: The notion of an \(\varepsilon\)-space is introduced as follows. A Tikhonov space \(X\) is called an \(\varepsilon\)-space if each Baire set \(E\) of \(\beta X\) disjoint from \(X\) is a subset of a countable union \(C\) of zero-sets of \(\beta X\) such that \(C\cap X= \emptyset\). Properties of \(\varepsilon\)-spaces are investigated. Consideration of \(\varepsilon\)-spaces is motivated by the observation that \(X\) is an \(\varepsilon\)-space iff the epicomplete epireflection of \(C(X)\) within a certain category of \(\ell\)-groups is just the \(\ell\)-group of Baire functions on \(X\).
Mathematics Subject Classification ID: 54D40
Mathematics Subject Classification ID: 54C30
Mathematics Subject Classification ID: 06F20
Mathematics Subject Classification ID: 46E25
zbMATH DE Number: 878060
zbMATH Keywords: epsilon-space
zbMATH Keywords: Stone-Čech compactification
zbMATH Keywords: Baire functions
reviewed by: R. G. Woods
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072193
OpenAlex ID: W4248467747
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DOI: 10.1216/RMJM/1181072193
description: scientific article; zbMATH DE number 878060