This is not a homework but it is a question in my mind.please guide me. Let X and Y be topological spaces,let f : X -----> Y is a function. when the following statements are equivalent????: 1) f is continuous 2) f(A') is subset of f(A)' ,for every A subset of X. Symbols: A' i.e limit points set of A ,and f(A)' i.e limit points set of f(A). pointing out: look to theorem 18-1 (page 104) from Munkres's book (TOPOLOGY 2edition 2000) and exercise 2 (page 111) from Munkres's book.