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 $\mathsf{Met}$ of quantale-valued metric spaces and uniformly continuous maps, with the essential requirement that the quantales are contin…