On singletoness of uniquely remotal sets (Q1088113)

The well known fact, that every uniquely remotal subset in a finite dimensional Hilbert space is necessarily a singleton, is generalized in the following ways: Let G be a bounded subset of a finite dimensional Hilbert space (or a nearly compact subset of an infinite dimensional Hilbert space). If the closure \(\bar G\) of G admits a unique farthest point to its Chebyshev center, then G is a singleton.