Hausdorff closed extensions of pre-uniform spaces

Abstract

The family of densely finite open covers of a Hausdorff space X determines a completable pre-uniformity on X and the canonical completion X is Hausdorff closed. We compare X with the Katetov extension kX of X and give sufficient conditions for the non-equivalence of kX and X.

Keywords

• Hausdorff closed space
• Densely finite-cover
• Katetov extension
• Round filter