We study classes of continuous functions on Rn that can be approximated in various degree by uniformly continuous ones (uniformly approachable functions). It was proved in [BDP1: A. Berarducci, D. Dikranjan, and J. Pelant, Functions with distant fibers and uniform continuity, preprint] that no polynomial function can distinguish between them. We construct examples that distinguish these classes (answering a question from [BDP1]) and we offer appropriate forms of uniform approachability that enable us to obtain a general theorem on coincidence in the class of all continuous functions.
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Last modified June 20, 2001.