Proximinality and Diametrically Maximal Sets in $C(K)$

Abstract

Abstract. We are concerned in this note with two optimization problems associated with diametrically maximal sets in spaces of continuous functions. Given an intersection of closed balls C ⊂ C(K), we show that there is an optimal solution to: i) the problem of minimizing dist(C, E) where E is any diametrically maximal set satisfying diam E = diam C, ii) the same problem removing the constraint diam E = diam C. We provide a characterization of the uniqueness of solution in the first problem.