5. (a) Let (X, d) be a metric space. Consider the metric space (XXX, 61*) where d*((m, y), (u, v)) = max{d(x, u), d(y, 11)} (see Homework 5 Problem 1.) Show that the original metric d : X X X > IR is a uniformly continuous real-valued function on the metric space X x X. (b) Let E be a nonempty compact subset of X , and let 6 = sup{d($, y) : :13, y E E}. Use part (a) and Homework 5 Problem 1(d) to prove that there exist ray 6 E such that d(:t, y) = 5 (cf. Homework 4 Problem 3.)