ABSTRACT
Let (M,ρ) be a metric space. By BM (x, r), we denote the closed ball centered at x ∈M with radius r > 0:
BM (x, r) = {y ∈M : ρ(x, y) ≤ r} . By SM (x, r), we denote the sphere centered at x ∈M with radius r > 0:
SM (x, r) = {y ∈M : ρ(x, y) = r} . As usual, we shall drop the subscript when M is clear from the context. For a subset A of (M,ρ), diam(A) denotes the diameter of A; that is,
diam(A) = sup {ρ(x, y) : x, y ∈ A} .
