Let C[0, 1] denote the collection of all continuous real-valued functions on the interval [0, 1], and define d(f, g) = supxeo, If(x) - g(x) | for functions f, g E C[0, 1]. (a) Prove that (C[0, 1], d) is a metric space. (b) Let A be the collection of all positive-valued functions in C(0, 1]. Is A open or closed? What is the set of limit points of A