3.) Let A C R. Define A, called the interior of A, by A" = {re A: there exists r > 0 such that (r - r,atr) C (a) Prove that A" is open. (b) Prove that A is open if and only if A = A". (c) Prove that (40) = A". (d) Prove that if B C A and B is open, then B C A. (e) Prove that A = U[ B : B is open and B C A}