5. Let K be a compact set on the metric space (X,d) and g: X > R continuous functions such that 9(93) > 0 and f(93) > 0 for all x E K. (a) Show that there exist positive constants Cl, 02 such that le(a:) S 9(33) S 02f($) for all a: E K. (b) Let (X, ||.||) be a normed space and let us denote by 6B the boundary of the closed unit ball (SB : {30 E X|||:1:||: 1}. Two norms ||.||1 and ||.||2 on X are said to be equivalent if there are positive con stants 01,02 such that: Clllmlll S \"IIIII2 S Cz||$||1 for all (I? E 63. Prove that any two norms on R'\" : (Rh, | D are equivalent for any k : 1,2,. . . . (c) Show an example of an innite dimensional normed vector space (X, ||.||) over R with two non-equivalent norms \"H1 and ||..||2