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Research Report CS-RR-293

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S.J. O'Neill, Partial Metrics, Valuations and Domain Theory (October 1, 1995).

Abstract

In this paper we develop some connections between the partial metrics of Matthews and the topological aspects of domain theory. We do this by introducing the valuation spaces, which are a special class of partial metric spaces. We develop the natural duality of partial metrics and propose that a natural context in which to view a partial metric space is as a bitopological space. We then see that successive conditions on a valuation can ensure that the pmetric topology is first of all order consistent (with the underlying poset), then equivalent to the Scott topology, and finally that the induced metric topology is equivalent to the patch topology.

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S.J. O'Neill, "Partial Metrics, Valuations and Domain Theory", Proceedings of the 11th Summer Conference on General Topology and Applications, Annals of the New York Academy of Sciences, ed. S. Andima and others, pp. 304-315 (1997)

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