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## Homework Statement

(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!