I'm learning about compact sets in topology and have problems doing the following exercise:

Let $C$ be a collection of closed compact sets in a topological space $X$ and let $U \subseteq X$ be open such that $\bigcap\_{A \in C} A \subseteq U$. Show that there exists a finite subcollection $C' \subseteq C$ such that $\bigcap\_{A \in C'} A \subseteq U$.