On singletonness of uniquely remotal sets
An unsolved problem in approximation theory is: if every point of a normed linear space X admits a unique farthest point in a given bounded set K, then must K be a singleton? In this paper an affirmative answer to the question is given for totally bounded nearly compact sets in complete locally convex linear metric spaces. For earlier work, see \textit{J. Blatter} [Rev. Roum. Math. Pure Appl. 14, 615-621 (1969; Zbl 0205.123)].
scientific article; zbMATH DE number 4214656