Quasicompactness and functionally Hausdorff spaces

Abstract

In [1] Van Est and Freudenthal introduced and studied several new separation axioms for a topological space. One of these was thepτsq axiom: Given distinct pointspandqofX, there exists a real continuous functionfonXwithf(p) ≠f(q). They observed that thepτsqaxiom lies strictly between the Hausdorff and completely regular axioms, and that it neither implies nor is implied by theT3axiom.