I'm given the following problem: Suppose that for every $n\in \mathbb{N}$ $V_n$ is a non-empty, closed subset of a compact space $X$, with $V_n \supseteq V_{n+1}$. Now I have to show that $V_{\infty}= \bigcap_{n=1}^{\infty} V_n \neq \emptyset$. How can I do that? I know the nested interval p...