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A uniform convergence for non-uniform spaces. (English) Zbl 0879.54003
“Strong convergence” is a pretopology defined on the set of functions from an arbitrary set \(X\) into a topological space \(Y\); it is generally finer than uniform convergence and preserves continuity. The “uniform” nature of strong convergence is demonstrated by showing how it can be derived from a certain filter \({\mathcal R}\) defined on \(Y \times Y\) which is, however, generally not a uniformity nor even a uniform convergence structure (in the sense of Cook and Fischer), as the authors seem to suggest. Various properties of strong convergence are studied, including conditions for strong convergence to coincide with uniform convergence.
Reviewer: D.C.Kent (Pullman)

54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
54E15 Uniform structures and generalizations