Physical Sciences and Mathematics Commons^™

A Note On Hausdorff Separation, Edwin Halfar

Department of Mathematics: Faculty Publications

The examples usually given as instances of topological spaces that have T₁-separation but not T₂-separation (Hausdorff) also have the property that some compact subset is not closed. This with the classic result concerning closedness of compact subsets of a Hausdorff space suggests the question of the equivalence of Hausdorff separation and the condition that the class of compact subsets be a subclass of the class of the closed subsets of a given space. The following is a simple result of this type and may be of some use in an introductory course in point set topology. …