.3. (a) Let C[0, 1] be the set of all continuous R-valued functions defined on the interval [0, 1]. (i) Show that the function dı : C[0, 1] < C[0, 1] → R defined by dı(f,g) := So \f (x) – g(x)|dx is a metric. = [4 points] (ii) Given f e C[0, 1] and € > 0, describe geometrically the open- e-ball Be(f) with respect to d1-metric. [4 points] (b) Let A be a subset of a metric space (R, d). Show that a A 0 if and only if A is both open and closed. [7 points]