Shape invariance of \(\mathbb{N}\)-compactifications
type: Item
instance of: scholarly article
title: Shape invariance of \(\mathbb{N}\)-compactifications
zbMATH Open document ID: 0806.54017
DOI: 10.1016/0166-8641(94)90109-0
published in: Topology and its Applications
publication date: 1995-02-14T00:00:00Z
review text: Let \(N\) denote the natural numbers with the discrete topology. In this paper a space is 0-dimensional if it has a base of clopen sets. A 0- dimensional space \(X\) has a unique \(N\)-compactification, \(\nu (X)\), which is characterized by the property that if \(f : X \to N\) is continuous, then there is a unique extension \(\widetilde f : \nu (X) \to N\). The authors use \(N\)-compactifications of 0-dimensional spaces to obtain a new shape invariant for all topological spaces. They give examples to show that the shape and topological classifications are not the same in the realm of 0-dimensional Tikhonov spaces. The authors do give some classes of spaces where it is true that having the same shape is equivalent to being homeomorphic within the given class of spaces.
Mathematics Subject Classification ID: 54C56
Mathematics Subject Classification ID: 54D35
zbMATH DE Number: 527423
zbMATH Keywords: \(N\)-compactification
zbMATH Keywords: shape invariant
author: Manuel A. Morón
author: Francisco R. Ruiz del Portal
author: José Sanjurjo
reviewed by: J. Keesling
MaRDI profile type: Publication
full work available at URL: 0166-8641(94)90109-0
OpenAlex ID: W2070512024
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description: scientific article; zbMATH DE number 527423