(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.
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!