Cantor's Intersection Theorem with closed sets Cantor's Intersection Theorem states that "if $\{C_k\}$ is a sequence of non-empty, closed and bounded sets satisfying $C_1 \supset C_2 \supset C_3 \dots$, then $\bigcap_{n \ge 1} C_n$ is nonempty.
If the term "compact sets" is replaced by "closed sets", the statement is not true. It makes sense to me, but couldn't find such a counterexample for it.

Consider the sequence $C_n = [n, \infty)$.
