\( \newcommand{\cat}[1] {\mathrm{#1}} \newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})} \newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}} \)

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 \( \bigcap_{n=1}^{\infty} F_n \neq \emptyset \).