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Totally bounded spaces and compact ordered spaces as domains of computation. (English) Zbl 0733.54024

Topology and category theory in computer science, Proc. Conf., Oxford/UK 1989, 207-229 (1991).
[For the entire collection see Zbl 0725.00017.]
The main aim of this interesting article is to contribute to the discussion of ‘convenient categories for computation’. The author argues that, in searching for ‘the’ category of domains of computation, the (bi)complete totally bounded quasi-(pseudo-)metric \(T_ 0\)-spaces, along with certain closely related categories (for instance the compact ordered spaces) are worthy of consideration. He shows that in many cases computational examples can help to clarify the general theory of limits and completeness in quasi-(pseudo-)metric and quasi-uniform spaces. He also carefully indicates the computer science motivation for the studied quasi-uniform concepts. As an application of his theory he proposes a construction of the (so-called) power space as a free semilattice, generalizing the Plotkin power domain and the Vietoris hyperspace. Most mathematical results are presented in a fairly sketchy fashion; a fuller account will be published elsewhere.
Reviewer: H.P.Künzi (Bern)

MSC:

54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
54E15 Uniform structures and generalizations
68Q55 Semantics in the theory of computing

Citations:

Zbl 0725.00017