On the Wallman-Frink compactification of 0-dimensional spaces and shape
type: Item
instance of: scholarly article
title: On the Wallman-Frink compactification of 0-dimensional spaces and shape
zbMATH Open document ID: 0761.54015
DOI: 10.1007/BF01292931
published in: Archiv der Mathematik
publication date: 1992-09-27T00:00:00Z
review text: We construct functors from the shape category (for metrizable spaces) to other categories. These functors allow us to obtain new shape invariants. On the other hand, we give a relation between the Stone-Čech compactification of two metrizable spaces with the same shape. Finally we prove the following result: ``Two metrizable spaces \(X,Y\) such that \(\text{ind}(X)=\text{ind}(Y)=0\) are of the same shape if and only if they are homeomorphic''. This result is a generalization of a theorem due to \textit{G. Kozlowski} and \textit{J. Segal} [Fundam. Math. 83, 151-154 (1974; Zbl 0269.54027)] (in the metrizable case).
Mathematics Subject Classification ID: 54C56
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 54F50
zbMATH DE Number: 62266
zbMATH Keywords: mutation
zbMATH Keywords: space of quasicomponents
zbMATH Keywords: Wallman-Frink compactification of a 0-dimensional space
zbMATH Keywords: shape invariants
author: Manuel A. Morón
MaRDI profile type: Publication
cites work: Quasicompactifications and shape theory
cites work: Über nulldimensionale Räume
cites work: On shape
cites work: Q4137750
cites work: On the shape of 0-dimensional paracompacta
cites work: Shapes for topological spaces
cites work: Q5686670
cites work: Nonequality of Dimensions for Metric Spaces
full work available at URL: https://doi.org/10.1007/bf01292931
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description: scientific article; zbMATH DE number 62266