Homeomorphisms of compact sets in certain Hausdorff spaces
type: Item
instance of: scholarly article
title: Homeomorphisms of compact sets in certain Hausdorff spaces
zbMATH Open document ID: 1226.54027
DOI: 10.1155/2011/493290
author: Arthur D. Grainger
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2011-09-09T00:00:00Z
review text: Let \(X=\{x_0\}\dot{\cup} V\dot{\cup} W\), with \(W\) infinite, and topologise \(X\) by the discrete topology on \(X\setminus\{x_0\}\) while basic neighbourhoods of \(x_0\) are of the form \(F\cup\{x_0\}\) where \(F\) ranges through the cofinite subsets of \(W\). Compact subsets of \(X\) are identified and are shown to be mutually homeomorphic if and only if they are of the same cardinality.
reviewed by: David B. Gauld
Mathematics Subject Classification ID: 54D30
Mathematics Subject Classification ID: 54A25
zbMATH DE Number: 5946478
zbMATH Keywords: compact subsets
Wikidata QID: Q58687829
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/493290
OpenAlex ID: W2107529887
cites work: Q4775958
cites work: Q3218111
cites work: Q4519564
cites work: Q4485837
description: scientific article; zbMATH DE number 5946478