On Chebyshev centers in metric spaces

Abstract

A Chebyshev center of a set A in a metric space (X, d) is a point of X best approximating the set A i.e., it is a point x 0 ∈ X such that sup y∈A d(x 0 , y) = inf x∈X sup y∈A d(x, y). We discuss the existence and uniqueness of such points in metric spaces thereby generalizing and extending several known result on the subject.