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A quantitative computational model for complete partial metric spaces via formal balls. (English) Zbl 1172.06003
The authors present a computational model for partial metric spaces that generalizes and unifies existing work in the literature. Given a partial metric space $(X,p)$, they use $({\Bbb B}X,\sqsubseteq_{d_p})$ to denote the poset of formal balls of the associated quasi-metric space $(X,d_p).$ They prove that a partial metric space $(X,p)$ is complete if and only if the poset $({\Bbb B}X,\sqsubseteq_{d_p})$ is a domain. Moreover, $(X,p)$ is complete and sup-separable if and only if $({\Bbb B}X,\sqsubseteq_{d_p})$ is an $\omega$-domain. Furthermore, with the help of the concept of a partial quasi-metric, for any complete partial metric space $(X,p)$ they construct a Smyth complete quasi-metric $q$ on ${\Bbb B}X$ that extends the quasi-metric $d_p$ such that both the Scott topology and the partial order $\sqsubseteq_{d_p}$ are induced by $q.$

##### MSC:
 06B35 Continuous lattices and posets, applications 54E35 Metric spaces, metrizability 68Q55 Semantics
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