The \(\delta\)-completion of a quasi-pseudometric space (Q2344326)

The authors present a completion theory for quasi-pseudometric spaces based on the concept of a so-called \(\delta\)-cut (that is, an ordered pair consisting of a family of right \(K\)-Cauchy filters and a family of left \(K\)-Cauchy filters which satisfies a list of conditions). The theory is clearly related to the theory of the \(\kappa\)-completion introduced by Andrikopoulos, which works with sequences. Some connections with the theory of the \(B\)-completion due to Makitu and Künzi are mentioned. All these theories are using ideas originating with Doitchinov, which can be motivated by the construction of the Dedekind-MacNeille completion of a partially ordered set. It may be interesting to investigate possible connections between these completion theories.