Approximation of Metric Spaces by Partial Metric Spaces

Reinhold Heckmann

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.

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


[Paper.ps.gz (13p, 36k)]


Reinhold Heckmann / heckmann@absint.com