Let the usual metric Define a function T : 1]) denote the set of continuous functions on [0, 1]. We endow it with d(f, g) sup If (t) T [f]@) f(t)dt. Let C C([O, 1]) be a bounded set. (a) Show that T is a continuous function. (b) Show that the set T (K) is a compact subset of C([O, 1]). Let the usual metric Define a function T : 1]) denote the set of continuous functions on [0, 1]. We endow it with d(f, g) sup If (t) T [f]@) f(t)dt. Let C C([O, 1]) be a bounded set. (a) Show that T is a continuous function. (b) Show that the set T (K) is a compact subset of C([O, 1]).