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Complete partial metric spaces have partially metrizable computational models. (English) Zbl 1243.68181
Summary: We show that the domain of formal balls of a complete partial metric space ($X, p$) can be endowed with a complete partial metric that extends $p$ and induces the Scott topology. This result, that generalizes well-known constructions of {\it A. Edalat} and {\it R. Heckmann} [Theor. Comput. Sci. 193, No. 1--2, 53--73 (1998; Zbl 1011.54026)] and {\it R. Heckmann} [Appl. Categ. Struct. 7, No. 1--2, 71--83 (1999; Zbl 0993.54029)] for metric spaces and improves a recent result in [the first and last author, Math. Struct. Comput. Sci. 19, No. 3, 541--563 (2009; Zbl 1172.06003)], motivates a notion of a partially metrizable computational model which allows us to characterize those topological spaces that admit a compatible complete partial metric via this model.
MSC:
68Q05Models of computation (Turing machines, etc.)
54E50Complete metric spaces
06A06Partial order
06B35Continuous lattices and posets, applications
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