Partial metrizability in value quantales

A characterization of partial metrizability: domains are quantifiable

A characterization of partial metrizability is given which provides a partial solution to an open problem stated by Künzi in the survey paper Nonsymmetric Topology ([Kün93], problem 71). The characterization yields a powerful tool which establishes a correspondence between partial metrics and special types of valuations, referred to as Q-valuations (cf. also [Sch00]). The notion of a Q-valuatio...

Resolvable Maps Preserve Complete Metrizability

Let X be a Polish space, Y a separable metrizable space, and f : X → Y a continuous surjection. We prove that if the image under f of every open set or every closed set is resolvable, then Y is Polish. This generalizes similar results by Sierpiński, Vainštain, and Ostrovsky.

Metrizability of Decomposition Spaces

Remarks on Metrizability

In connection with those paragraphs of my paper Applications of the theory of Boolean rings to general topology (Trans. Amer. Math. Soc. vol. 41 (1937) pp. 375-481) dealing with regular spaces, I have long been curious to know whether certain results proved there could be used to obtain the well known theorem that a separable (Hausdorff) space is metrizable if (and only if) it is regular. Since...

Quantales and Observational Semantics

We illustrate the idea that quantales can be regarded as algebras of experimental observations on physical systems, and we give a survey of some research in computer science where this idea has been used. We extend the mathematical framework hitherto available so that it can be applied to more general systems than before, in particular to quantum systems and systems whose behaviour is partially...