Farthest point theory is not so rich and developed as nearest point theory, which has more applications. Farthest points are useful in studying the extremal structure of sets; see, e.g., the survey paper . There are some interactions between the two theories; in particular, uniquely remotal sets in Hilbert spaces are related to the old open problem concerning the convexity of Chebyshev sets. The aim of this paper is twofold: first, we indicate characterizations of inner product spaces and of infinite-dimensional Banach spaces, in terms of remotal points and uniquely remotal sets. Second, we try to update the survey paper , concerning uniquely remotal sets.
"REMOTAL SETS REVISITED." Taiwanese J. Math. 5 (2) 367 - 373, 2001. https://doi.org/10.11650/twjm/1500407343