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Partial metric monoids and semivaluation spaces. (English) Zbl 1084.22002
The authors discuss the importance of stable partial metric meet semilattices in quantitative domain theory. In particular they show that the interval domain, the domain of words and the dual complexity space can be modelled as stable partial metric monoids, where a stable partial metric monoid is a partial metric monoid (X,·,p) such that (X,p) is a stable partial metric meet semilattice. They also introduce the notion of a semivaluation monoid and prove that there is a bijection between stable partial metric monoids and semivaluation monoids.
MSC:
22A15Structure of topological semigroups
22A26Topological lattices, lattices and applications (topological groups)
54E35Metric spaces, metrizability
54H12Topological lattices (topological aspects)
68Q55Semantics