Question 1: a) Let R denotes the real line and let Tz denotes the subspace topology...

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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]] 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]]