Prove the empty set is closed for a metric space (X,d). I'm not sure how to approach the proof for this. I know this statement is vacuously true, because the empty set does not contain any accumulation points. But I'm having a hard time writing a proof for this. I have looked at other answers on here, however we have not learned what a "ball" is in lecture. 

A set is closes iff its complement is open. The complement of the empty set is the whole space which is open in itself.
