Past exam of the Probability, statistics and options II course of the University of Oxford / 2008 / E / 4 / a / Solution

In the usual real line take $\boxed{F_n=[n,\infty )}$. Each set is nonempty and closed, and $F_{n+1}\subseteq F_n$. No real number lies in them all, because the positive integers are unbounded. Thus their intersection is empty. These sets are not compact.