6 papers
Robustness Analysis via Horofunction Compactification
Harrison Bennett, Amin Farjudian
Robustness analysis plays a central role in the verification and design of computational and hybrid systems, particularly when system behaviour depends continuously on parameters s…
Metrization of Quasi-Uniformities, Powerset Monads, and Qualitative Robustness Analysis
Francesco Dagnino, Amin Farjudian, Eugenio Moggi
We study the relationship between quasi-uniform spaces, topological spaces, and quantale-valued metric spaces. Our main result is a metrization theorem establishing an equivalence…
A Domain-Theoretic Foundation for Imprecise Probability and Credal Sets
Abbas Edalat, Pietro Di Gianantonio, Amin Farjudian
We develop a domain-theoretic framework for imprecise probability reasoning and inference on general topological spaces with a countably based continuous lattice of open sets. We a…
Robust Topology and the Hausdorff-Smyth Monad on Metric Spaces over Continuous Quantales
Francesco Dagnino, Amin Farjudian, Eugenio Moggi
We define a (preorder-enriched) category of quantale-valued metric spaces and uniformly continuous maps, with the essential requirement that the quantales are contin…
Continuous Domains for Function Spaces Using Spectral Compactification
Amin Farjudian, Achim Jung
We introduce a continuous domain for function spaces over topological spaces which are not core-compact. Notable examples of such topological spaces include the real line with the…
Robustness in Metric Spaces over Continuous Quantales and the Hausdorff-Smyth Monad
Francesco Dagnino, Amin Farjudian, Eugenio Moggi
Generalized metric spaces are obtained by weakening the requirements (e.g., symmetry) on the distance function and by allowing it to take values in structures (e.g., quantales) tha…