Totally bounded spaces and compact ordered spaces as domains of computation
Topology and category theory in computer science
Dynamical systems, measures, and fractals via domain theory
Information and Computation
Selected papers of the workshop on Topology and completion in semantics
A computational model for metric spaces
Theoretical Computer Science
Computable banach spaces via domain theory
Theoretical Computer Science - Special issue on computability and complexity in analysis
Semi-Lipschitz functions and best approximation in quasi-metric spaces
Journal of Approximation Theory
On the Yoneda completion of a quasi-metric space
Theoretical Computer Science
Quasi Uniformities: Reconciling Domains with Metric Spaces
Proceedings of the 3rd Workshop on Mathematical Foundations of Programming Language Semantics
A characterization of partial metrizability: domains are quantifiable
Theoretical Computer Science - Topology in computer science
Mathematical Structures in Computer Science
The correspondence between partial metrics and semivaluations
Theoretical Computer Science - Mathematical foundations of programming semantics
Partial metrisability of continuous posets
Mathematical Structures in Computer Science
Generalized ultrametric spaces in quantitative domain theory
Theoretical Computer Science
Theoretical Computer Science - Spatial representation: Discrete vs. continous computational models
The space of formal balls and models of quasi-metric spaces
Mathematical Structures in Computer Science
Sequence spaces and asymmetric norms in the theory of computational complexity
Mathematical and Computer Modelling: An International Journal
Domain theoretic characterisations of quasi-metric completeness in terms of formal balls†
Mathematical Structures in Computer Science
The formal ball model for -categories
Mathematical Structures in Computer Science
Coupled fixed point results for (ψ,φ)-weakly contractive condition in ordered partial metric spaces
Computers & Mathematics with Applications
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Given a partial metric space (X, p), we use (BX, ⊑dp) to denote the poset of formal balls of the associated quasi-metric space (X, dp). We obtain characterisations of complete partial metric spaces and sup-separable complete partial metric spaces in terms of domain-theoretic properties of (BX, ⊑dp). In particular, we prove that a partial metric space (X, p) is complete if and only if the poset (BX, ⊑dp) is a domain. Furthermore, for any complete partial metric space (X, p), we construct a Smyth complete quasi-metric q on BX that extends the quasi-metric dp such that both the Scott topology and the partial order ⊑dp are induced by q. This is done using the partial quasi-metric concept recently introduced and discussed by H. P. Künzi, H. Pajoohesh and M. P. Schellekens (Künzi et al. 2006). Our approach, which is inspired by methods due to A. Edalat and R. Heckmann (Edalat and Heckmann 1998), generalises to partial metric spaces the constructions given by R. Heckmann (Heckmann 1999) and J. J. M. M. Rutten (Rutten 1998) for metric spaces.