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Probabilistic convergence spaces and generalized metric spaces. (English) Zbl 0905.54005

Before topologies were defined via open set axioms or in other equivalent ways, M. Fréchet had already introduced metric spaces and (sequential) convergence spaces. Although metric spaces do not determine a subcategory of either the topological or convergence space categories, they are embedded in the category of probabilistic convergence spaces. This interesting paper makes use of the latter result to characterize infinity-valued metric spaces and some of their most natural generalizations entirely in terms of convergence criteria.
Reviewer: D.C.Kent (Pullman)

MSC:

54B30 Categorical methods in general topology
54E70 Probabilistic metric spaces
54A05 Topological spaces and generalizations (closure spaces, etc.)
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
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