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Zbl 1084.22002
Partial metric monoids and semivaluation spaces.
(English)
[J] Topology Appl. 153, No. 5-6, 948-962 (2005). ISSN 0166-8641

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 $(X,\cdot,p)$ 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.
[Hans Peter Künzi (Rondebosch)]
MSC 2000:
*22A15 Structure of topological semigroups
22A26 Topological lattices, etc. (topological groups)
54E35 Metric spaces, metrizability
54H12 Topological lattices (topological aspects)
68Q55 Semantics

Keywords: partial metric monoid; quasi-metric; weightable; meet semilattice; semivaluation; interval domain; domain of words; dual complexity space

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