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New concepts related to approximating a Lipschitz function between Banach spaces by aane functions are introduced. Results which clarify when such approximations are possible are proved and in some cases a complete characterization of the spaces X, Y for which any Lipschitz function from X to Y can be so approximated is obtained. This is applied to the(More)
It is a well-known result of Kadec that every two separable infinite dimensional Banach spaces are homeomorphic. Also in large classes of nonseparable Banach spaces (perhaps all) the density character of a Banach space is its only topological invariant (see the book [2] for details). The situation changes considerably if we consider uniform homeomorphisms.(More)
We give several sufficient conditions on a pair of Banach spaces X and Y under which each Lipschitz mapping from a domain in X to Y has, for every ǫ > 0, a point of ǫ-Fréchet differentiability. Most of these conditions are stated in terms of the moduli of asymptotic smoothness and convexity, notions which appeared in the literature under a variety of names.(More)
Corrigendum Corrigendum to " Best approximation in polyhedral Banach spaces " [J. Abstract The present note is a corrigendum to the paper " Best approximation in polyhedral Banach spaces " , J. Professor G. Godefroy kindly pointed out to us that the implication " if P Y is H-u.s.c. on its effective domain then Y is relatively strongly proximinal " in [1,(More)