Question 1: a) Let R denotes the real line and let Tz denotes the subspace topology of Z. Prove that Tz=P(Z) b) Let X be a topological space and let A be an open subset of X. (i) Prove that for any BC X we have ANBCAN B. (ii) Suppose A is an open subspace of X. Use (i) to show that for each a E A and each VE NA(a) we have VEN(a). [(4,(6,4]]