Approximation of Metric Spaces by Partial Metric Spaces |
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Authors: | Reinhold Heckmann |
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Affiliation: | (1) FB 14 – Informatik, Universität des Saarlandes, Postfach 151150, 66041 Saarbrücken, Germany |
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Abstract: | Partial metrics are generalised metrics with non-zero self-distances. We slightly generalise Matthews' original definition of partial metrics, yielding a notion of weak partial metric. After considering weak partial metric spaces in general, we introduce a weak partial metric on the poset of formal balls of a metric space. This weak partial metric can be used to construct the completion of classical metric spaces from the domain-theoretic rounded ideal completion. |
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Keywords: | generalised metric spaces domains Scott topology preorder |
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