Partial metric monoids and semivaluation spaces

Abstract

Stable partial metric spaces form a fundamental concept in Quantitative Domain Theory. Indeed, all domains have been shown to be quantifiable via a stable partial metric.Monoid operations arise naturally in a quantitative context and hence play a crucial role in several applications. Here, we show that the structure of a stable partial metric monoid provides a suitable framework for a unified approach to some interesting examples of monoids that appear in Theoretical Computer Science. We also introduce the notion of a semivaluation monoid and show that there is a bijection between stable partial metric monoids and semivaluation monoids.

Characterizations of partial metric completeness in terms of weakly contractive mappings having fixed point

“…Since then partial metric spaces have turned into a very efficient tool in constructing computational models for metric spaces and other related structures via domain theory (see [12,22,24,25,27,32,33], etc. ).…”

A coincident point and common fixed point theorem for weakly compatible mappings in partial metric spaces

“…He introduced this notion to solve some difficulties of the domain theory and showed the Banach's contraction principle [7] can be generalized in context of partial metric spaces for applications in program verifications (see for example [13,21,24,27,31,32,33,36]. Now, we recall definition and properties of partial metric spaces.…”

Common fixed points of Ciric-type contractions on partial metric spaces

“…Other examples of partial metric spaces which are interesting from a computational point of view may be found in [16,21,22,26,30].…”