O96 : 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 in a valation can ensure that the
partial metric 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.