1. Let A, B be subsets of a metric space (M, d) so that A C B C A. Prove or disprove: (i) If A is connected, so is B. (ii) If B is connected, so is A. 2. Let (M, d) be a metric space. Show that the space loo (M) := {f : M -+ : f has bounded range } of bounded real valued functions on M is complete under the norm 1Iflloo : = sup If ( 20)1 (f E loo ( M ) ). TEM Show that the set A = {f El1 : If(n)|