Concerning completeness of the fine quasi-uniformity

Abstract

[EN] A quasi-uniform space (X,U) is called strongly complete if every stable filter on (X, U-1) has a cluster point and it is called hypercomplete if every stable filter on (X,U) has a cluster point. We show, among other things, that the fine quasi-uniformity of each topological space is strongly complete and that the fine quasi-uniformity of each topological space that admits a point symmetric quasi-pseudometric is hypercomplete.