On nearly Hausdorff compactifications

Abstract

We introduce and study here the notion of nearly Hausdorffness, a separation axiom, stronger than T1 but weaker than T2. For a space X, from a subfamily of the family of nearly Hausdorff spaces, we construct a compact nearly Hausdorff space rX containing X as a densely C*-embedded subspace. Finally, we discuss when rX is βX.

Keywords

• Regular closed set
• Filter
• Compactification
• Wallman base