All topologies come from generalized metrics
American Mathematical Monthly
Handbook of logic in computer science (vol. 3)
Quasi Uniformities: Reconciling Domains with Metric Spaces
Proceedings of the 3rd Workshop on Mathematical Foundations of Programming Language Semantics
Generalized metrics and uniquely determined logic programs
Theoretical Computer Science - Topology in computer science
A characterization of partial metrizability: domains are quantifiable
Theoretical Computer Science - Topology in computer science
Static space–times naturally lead to quasi-pseudometrics
Theoretical Computer Science
A quantitative computational model for complete partial metric spaces via formal balls†
Mathematical Structures in Computer Science
Domain theoretic characterisations of quasi-metric completeness in terms of formal balls†
Mathematical Structures in Computer Science
On fixed points of strictly causal functions
FORMATS'13 Proceedings of the 11th international conference on Formal Modeling and Analysis of Timed Systems
An axiomatization of the theory of generalized ultrametric semilattices of linear signals
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
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Domains and metric spaces are two central tools for the study of denotational semantics in computer science, but are otherwise very different in many fundamental aspects. A construction that tries to establish links between both paradigms is the space of formal balls, a continuous poset which can be defined for every metric space and that reflects many of its properties. On the other hand, in order to obtain a broader framework for applications and possible connections to domain theory, generalized ultrametric spaces (gums) have been introduced. In this paper, we employ the space of formal balls as a tool for studying these more general metrics by using concepts and results from domain theory. It turns out that many properties of the metric can be characterized via its formal-ball space. Furthermore, we can state new results on the topology of gums as well as two new fixed point theorems, which may be compared to the Priesz-Crampe and Ribenboim theorem, and the Banach fixed point theorem, respectively. Deeper insights into the nature of formal-ball spaces are gained by applying methods from category theory. Our results suggest that, while being a useful tool for the study of gums, the space of formal balls does not provide the hoped-for general connection to domain theory.