For any two real numbers u and v, max(u, v) := u iff u ≥ v; otherwise, max(u, v) := v. A metric space (S, d) is called an ultrametric space and d an ultrametric if d(x, z) ≤ max(d(x, y), d(y, z)) for all x, y, and z in R. Show that in an ultrametric space, any open ball B(x, r ) is also closed.