Two Topologies Are Better than One
نویسنده
چکیده
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 bitopo-logical 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.
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