The δ-completion of quasi-pseudometric spaces

Abstract

Over many years much progress has been made in the investigation of completion theory of quasi-pseudometric spaces. In particular, Doitchinov, Kunzi, Salbany and others have published several articles concerning the concept of completion for quasi-pseudometric spaces. Recently, Andrikopoulos introduced the theory of к-completion which uses the pair of family of right к-Cauchy and left к-Cauchy sequences that he called к-cut. The aim of this dissertation is to begin a similar investigation by using the pair of family of right K-Cauchy and left K-Cauchy filters. It starts off with a summary of results obtained for the theory of bicompletion, B-completion and к-completion, which has been investigated in the past. We conclude by commencing an investigation of δ-completion. Here several results obtained for к-completion are generalized.