Exercise: nested sequences of sets

The following statement is [true or false?]

If $F_1\supseteq F_2\supseteq F_3\supseteq F_4\supseteq ...$ is a nested sequence of nonempty closed sets, then the intersection $\bigcap _{n=1}^{\mathrm{\infty }}{F}_n\ne \mathrm{\varnothing }$.