Chebyshev Radius and Centers

Abstract

For a bounded subset A of E and x ∈ E, let \( r\left( {x,A} \right) \equiv \mathop {\sup }\limits_{y \in A} \left\| {y - x} \right\| \) (the minimal radius of a ball centered at x and containing A). For G ⊂ E, \( {r_G}\left( A \right) \equiv \mathop {\inf }\limits_{y \in G} \left( {y,A} \right) \) is the (relative) Chebyshev radius of A in G, and Z G (A) = {y ∈ G; r(y, A) = r G (A)} is the (possible empty) Chebyshev center set of A in G.