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.