Homeomorphisms of compact sets in certain Hausdorff spaces
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.
scientific article; zbMATH DE number 5946478