Partial Metrics, Valuations and Domain Theory
by
Simon John O'Neill
University of Warwick

Partially ordered sets and metric spaces are used in studying semantics in Computer Science. Sets with both these structures are hence of particular interest. The partial metric spaces introduced by Matthews are an attempt to bring these ideas together in a single axiomatic framework.

In this talk, we will introduce the axioms, and propose that an appropriate context in which to consider these spaces is as a bitopological space, that is as a space with two (related) topologies. We then briefly cover the groundwork for a theory of partial metric spaces by generalising ideas from topology and metric spaces.

To apply this work to Computer Science we look at those partial metric spaces which are also domains. To do this, we introduce a special class of partial metrics, which are built from an auxillary function (a valuation) in much the same way as the metrics for normed spaces. We then present a cartesian closed subcategory of such spaces. We note that this work is not an attempt to generalise the domain theoretic and metric approaches to semantics, but rather an attempt to use them together.

Date received: April 12, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caae-60.