Cantor Intersection Theorem

The Cantor Intersection Theorem states:

If $F_{n}$ is a collection of closed subspaces of a complete metric space such that $F_{n+1}\in F_{n}$ for all $n$ and $\lim _{n\to \infty }diameter(F_{n})=0$, then ∩ $F_{n}$ is a single point.