On completely regular spaces for which \(eX=\beta X\)
type: Item
instance of: scholarly article
zbMATH Open document ID: 0974.54014
author: K. V. Matyushichev
publication date: 2001-07-30T00:00:00Z
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 54D15
Mathematics Subject Classification ID: 54B05
Mathematics Subject Classification ID: 54B10
zbMATH DE Number: 1626587
zbMATH Keywords: Stone-Čech compactification
zbMATH Keywords: semiregular compactification
MaRDI profile type: Publication
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title: On completely regular spaces for which \(eX=\beta X\)
published in: Trudy Petrozavodskogo Gosudarstvennogo Universiteta. Seriya Matematika
review text: Let \(eX\) be the largest semiregular compactification of \(X\) satisfying the following property: for any open cover of \(eX\) there exists a finite subfamily which is a cover of \(X\). It is known, that \(eX\neq \beta X\) for some completely regular space \(X\), therefore the property \(eX=\beta X\) defines a new class of completely regular spaces. In this paper, the author constructs three examples to show that this class is not closed under passage to infinite sums, subspaces and Cartesian products. The author introduces here a notion of countably regular spaces and considers some properties of countably regular spaces.
reviewed by: Aleksandr A. Ivanov
description: scientific article; zbMATH DE number 1626587