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Partial metrisability of continuous posets

In this article, we characterise all continuous posets that are partially metrisable in their Scott topology. We present conditions for pmetrisability, which are both necessary and sufficient, in terms of measurements, domain-theoretic bases and, in a more general setting, in terms of radially conve...

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Bibliographic Details
Published in:Mathematical structures in computer science 2006-04, Vol.16 (2), p.359-372
Main Author: WASZKIEWICZ, PAWEŁ
Format: Article
Language:English
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Summary:In this article, we characterise all continuous posets that are partially metrisable in their Scott topology. We present conditions for pmetrisability, which are both necessary and sufficient, in terms of measurements, domain-theoretic bases and, in a more general setting, in terms of radially convex metrics. These conditions, together with their refinements and generalisations, set a natural hierarchy on the class of partially metrised posets. We locate the class of countably-based continuous dcpos within this hierarchy.
ISSN:0960-1295
1469-8072
DOI:10.1017/S0960129506005196