The correspondence between partial metrics and semivaluations

Schellekens, Michel

doi:10.1016/j.tcs.2003.11.016

Cited by 96 publications

(53 citation statements)

References 12 publications

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“…In this section we introduce a particularly interesting subclass of partial symmetric spaces. Both partial metric spaces considered by Matthews [14], O'Neill [16,17], Schellekens [19,20], Heckmann [9] and Waszkiewicz [24] and semimetric spaces in Topology are our major examples of partial semimetric spaces.…”

Section: Distance Axiomsmentioning

confidence: 99%

The local triangle axiom in topology and domain theory

Waszkiewicz

2003

Appl. Gen. Topol.

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Abstract. We introduce a general notion of distance in weakly separated topological spaces. Our approach differs from existing ones since we do not assume the reflexivity axiom in general. We demonstrate that our partial semimetric spaces provide a common generalization of semimetrics known from Topology and both partial metrics and measurements studied in Quantitative Domain Theory. In the paper, we focus on the local triangle axiom, which is a substitute for the triangle inequality in our distance spaces. We use it to prove a counterpart of the famous Archangelskij Metrization Theorem in the more general context of partial semimetric spaces. Finally, we consider the framework of algebraic domains and employ Lebesgue measurements to obtain a complete characterization of partial metrizability of the Scott topology.2000 AMS Classification: 54E99, 54E35, 06A06.

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Section: Distance Axiomsmentioning

confidence: 99%

The local triangle axiom in topology and domain theory

Waszkiewicz

2003

Appl. Gen. Topol.

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“…For some more examples of partial metric spaces, we refer to [1,3,7,15,43,46]. Each partial metric p on X generates a T 0 topology τp on X which has as a base the family open p-balls {Bp(x, ε) : x ∈ X, ε > 0}, where Bp(x, ε) = {y ∈ X : p(x, y) < p(x, x) + ε}, for all x ∈ X and ε > 0.…”

Section: Introductionmentioning

confidence: 99%

Common fixed point results of four mappings in ordered partial metric spaces

Nazır

Silvestrov

Abbas

2016

Waves, Wavelets and Fractals

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On partially ordered set equipped with a partial metric, we study the sufficient conditions for existence of common fixed points of various mappings satisfying generalized weak contractive conditions. These results unify several comparable results in the existing literature. We also study the existence of nonnegative solution of implicit nonlinear integral equation. Furthermore, we study the fractal of finite family of generalized contraction mappings defined on a partial metric space.

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“…In fact, the partial metric spaces offer a suitable framework to model several distinguished examples of the theory of computation and also to model metric spaces via domain theory (e.g. [4,5,7,8,18,19,20,21,22,23,24]). In this direction, Aydi et al [1] introduced the concept of a partial Hausdorff metric and extended Nadler's fixed point theorem to the setting of partial metric spaces.…”

Section: Introductionmentioning

confidence: 99%