Let (X, d) be a metric space and let r be a real number with r > 0. Define p XxX → R by p(x, y) = rd(x, y).
(a) Prove that p is a metric on X.
(b) Show that a subset of X is open in (X, d) if and only if it is open in (X, p).
(c) Does it follow that for each AC X, inta(A) = int,(A)?
