Hey, I was just trying out some questions from Rudin, when I had this doubt as to whether my answer is right, can you please tell me ifI am right?
Let E' be the set of all limit points of a set E. Prove that E' is closed.
Let x be a limit point of E'. So every nbd of x contains infinitely many points of E'. But in every nbd of every point of E' are infinitely many points of E, since every point of E' is a limit point of E.
Thereby every nbd of x contains infinitely many points of E. So x is a limit point of E (ie) x is in E'.
Hence E' is closed. Am i right?