Categorical properties of probabilistic convergence spaces (Q1272545)

It is proved that the category of probabilistic pretopological (or pseudotopological) spaces is the extensional topological hull (or cartesian-closed extensional topological hull, resp.) of the category \(F_T\)-diagonal probabilistic convergence spaces for any triangular norm \(T\). As special cases one gets Lowens' corresponding results on approach spaces [\textit{E. Lowen} and \textit{R. Lowen}, Cah. Topologie Géom. Différ. Catégoriques 30, No. 3, 213-228 (1989; Zbl 0706.18002)].