Uniform approximation of vector-valued functions

Summary Uniform approximation of vector-valued functions is defined, together with analogs of extreme points and H-sets. Characterizations of best approximations are given in terms of these, and some applications are presented.Most of the work for this paper was done at Michigan State University, East Lansing; as a Ph. D. Thesis directed by D. G. MOURSUND. The author wishes to thank Prof. MOURSUND for his kind assistance.