We study classes of continuous functions on R that can be approximated in various degree by uniformly continuous ones (uniformly approachable functions). It was proved in [BDP1] 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 ...

EXPONENTIAL LAW FOR UNIFORMLY CONTINUOUS PROPER MAPS R . AYALA, E . DOMINGUEZ, A . QUINTERO The purpose of this note is to prove the exponential law for uniformly continuous proper maps . Let X be a regular space and Y a locally compact regular space . It is well known that the spaces of continuousmaps C(X x Y, Z) and C(X, C(Y Z)) are homeomorphic considering the compact-open topology. This pro...