The δ-completion of a quasi-pseudometric space

Abstract

We present a notion of completeness and a completion for a quasi-pseudometric space. In this article, we extend the construction of κ-completion of Andrikopoulos via Cauchy filter pairs which are not balanced in the sense of Künzi and Makitu [6]. We give an alternative illustration of the fact that on a quasi-pseudometric space, a convergent Cauchy filter pair need not be balanced.