The δ-completion of a quasi-pseudometric space

On the Yoneda completion of a quasi-metric space

Several theories aimed at reconciling the partial order and the metric space approaches to Domain Theory have been presented in the literature (e.g. Flagg and Kopperman, Theoret. Comput. Sci. 177 (1) (1997) 111–138; Bonsangue et al., Theoret. Comput. Sci. 193 (1998) 1–51; Symth, Quasi-Uniformities: Reconciling Domains with Metric Spaces, Lectures Notes in Computer Science, vol. 298, Springer, B...

On completeness of quasi-pseudometric spaces

The notion of completeness in metric spaces and that of completing a metric space are traditionally discussed in terms of Cauchy sequences. The main reason being that this concept deals precisely with the issue of convergence of sequences in the sense that every convergent sequence is a Cauchy sequence. The paper deals with completion in a setting that avoids explicit reference to Cauchy sequen...

Hyperspace of a fuzzy quasi-uniform space

The aim of this paper is to present a fuzzy counterpart method of constructing the Hausdorff quasi-uniformity of a crisp quasi-uniformity. This process, based on previous works due to Morsi cite{Morsi94} and Georgescu cite{Georgescu08}, allows to extend probabilistic and Hutton $[0,1]$-quasi-uniformities on a set $X$ to its power set.  In this way, we obtain an endofunctor for each one of the c...

A double completion for an arbitrary T0-quasi-metric space

We present a conjugate invariant method for completing any T0-quasi-metric space. The completion is built as an extension of the bicompletion of the original space. For balanced T0-quasi-metric spaces our completion yields up to isometry the completion due to Doitchinov. The question which uniformly continuous maps between T0-quasimetric spaces can be extended to the constructed completions lea...

On δ-Quasi Armendariz Modules