Completing Quasi-metric Spaces - an alternative Approach

Abstract

Abstract. We define a completion theory for all approach spaces with an underlying T0 topology, which agrees with the usual metric completion theory for metric spaces. Hence we can complete any quasi-metric space. Remarkably the completion of a quasi-metric space need not be quasi-metric, but can be a genuine approach space. The theory corresponds well with the (strict) completion of nearness spaces. 1.