1. The problem statement, all variables and given/known data Prove or disprove the following statement: The closure of a set S is closed. 2. Relevant equations Definition of closure: set T is the closure of set S means that T is the union of S and the set of limit points of S. Definition of a closed set: set S is closed means that if p is a limit point of S then p is in S. 3. The attempt at a solution So, the closure of set S-- call it set T-- contains all the elements of S and also all the limit points of S. Then, T must have limit points that is contained in it. I can't prove that all the limit points of T is in T. I can only prove that all the limit points of S is in T. Help?