please do this problem by following the giving hint and justify and complete all parts especially "the student should justify this" , thanks

4. If B = ball l", show that d($, y) = 2,2-||06) 0)| defines a metric on B and that this metric defines the weak-star topology on B. Hint: 5.5.4. Let T: (B, wk*) + (B,d) be the identity map. Let Y E B and > 0. Choose a positive integer N so that 2-N 4. Set U := {YE B:146- () 4 for j = 0,...,N}. Then the student should justify this) (0, 0) 0. Choose a positive integer N so that 2-N 4. Set U := {YE B:146- () 4 for j = 0,...,N}. Then the student should justify this) (0, 0)