AMBIGUOUS LOCI OF THE FARTHEST DISTANCE MAPPING FROM COMPACT CONVEX-SETS

Let E be a strictly convex separable Banach space of dimension at leas t 2. Let K(E) be the space of all nonempty compact convex subsets of E endowed with the Hausdorff distance. Denote by K0 the set of all X is -an-element-of K (E) such that the farthest distance mapping a bar arr ow pointing right M(X)(a) is multivalued on a dense subset of E. It is proved that K0 is a residual dense subset of K(E).