On Farthest Points

Section 2 of this paper deals with the generalizations of a theorem due to Motzkin, Straus and Valentine [7] and a theorem due to V. Klee [4]. Theorem 1 studies the continuity of the farthest point map in a matric space and Theorem 2 establishes that if a compact set in a Frechet space [9] is uniquely remotal with respect to the closure of its convex hull then the set is singleton.