3. Let S C R be any subset. We say that O C S is open in S if for every p E O there exists e > 0 s.t. (p-6, p+e)nS CO. We say that A C S is closed in S if and only if O = S\\ A is open in S. Prove: O C S is open in S if and only if there exists Of C R open so that O = Or n S. Prove: that the following statements are equivalent for a function f : S - R. (a) f is continuous. (b) The preimage under f of any open set is open in S. (c) The preimage under f of any closed set is closed in S