O'Neill, Simon (1995) Two topologies are better than one. University of Warwick. Department of Computer Science. (Department of Computer Science research report). (Unpublished)

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Abstract

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. We consider an appropriate context in which to consider these spaces is as a bitopological space, i.e. a space with two (related) topologies. From this starting point, we cover the groundwork for a theory of partial metric spaces by generalising ideas from topology and metric spaces. For intuition we repeatedly refer to the real line with the usual ordering and metric as a natural example. We also examine in detail some other examples of more relevance to Computer Science.

Item Type:	Report
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Computer Science
Library of Congress Subject Headings (LCSH):	Partially ordered sets, Metric spaces, Topology
Series Name:	Department of Computer Science research report
Publisher:	University of Warwick. Department of Computer Science
Official Date:	April 1995
Dates:	Date Event April 1995 Completion
Number:	Number 283
Number of Pages:	27
DOI:	CS-RR-283
Institution:	University of Warwick
Theses Department:	Department of Computer Science
Status:	Not Peer Reviewed
Publication Status:	Unpublished
Related URLs:	Organisation

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