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Categorical properties of probabilistic convergence spaces. (English) Zbl 0917.54003
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 [E. Lowen and R. Lowen, Cah. Topologie Géom. Différ. Catégoriques 30, No. 3, 213-228 (1989; Zbl 0706.18002)].
Reviewer: M.Hušek (Praha)

MSC:
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
54B30 Categorical methods in general topology
18B30 Categories of topological spaces and continuous mappings (MSC2010)
18B15 Embedding theorems, universal categories
54E70 Probabilistic metric spaces
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