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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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Published in: | Mathematical structures in computer science 2006-04, Vol.16 (2), p.359-372 |
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Main Author: | |
Format: | Article |
Language: | English |
Citations: | Items that cite this one |
Online Access: | Get full text |
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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. |
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ISSN: | 0960-1295 1469-8072 |
DOI: | 10.1017/S0960129506005196 |