Let (X,d) be metric space, A a subset of X and x in X. We will say that x is an accumulation point of A if for each we have . We denote the set of all accumulation points of A as A' Then, let (X,d) be metric space and A a subset of X

a) Prove that A' is a closed subset of X.
b) Prove that if X is a compact metric space and A is an infinite set, then A' is non-empty.