Approximation of Metric Spaces by Partial Metric Spaces

Reinhold Heckmann


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.

Key words: Generalised Metric Spaces, Domains, Scott Topology, Preorder

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Reinhold Heckmann /