1. The problem statement, all variables and given/known data (X,d) metric space, we have a sequence xn from n=1 to infinity G is a subset of X containing all cluster points of sequence xn. need to show that G is closed. 3. The attempt at a solution I tried to show that X\G is open. so take any point c in X\G, there exists an r>0 s.t. B(c;r) is contained in X\G. But I can't show how to do this. There might be another way to do this is that, if yn from n=1 to infinity is a convergen sequnce in G, then its limit is contained in G. But how could we construct such sequence, and show that its limit lies within G? need help pls. thanks!