A characterization of partial metrizability: domains are quantifiable

Schellekens, Michel

doi:10.1016/s0304-3975(02)00705-3

Cited by 91 publications

(59 citation statements)

References 23 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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“…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. ).…”

Section: Introductionmentioning

confidence: 99%