Hello, I have a real analysis question.

I need your help.

Thank you so much.

6) Given A C R", the derived set A' is the set of all Cluster points of A. (a) Prove that A' is Closed. (b) Prove that A = A U A'. (c) If A = A', A is sometimes said to be perfect. Give examples of perfect and nonperfect subsets of R\" (there are examples for any n E N, but feel free to provide examples for only one an E N). Given a set A C R" the closure of A is defined to be the intersection of all closed sets that contain A. The closure is denoted A