\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Counter-example: descending closed sets with empty intersection. For \(n \ge 0\), set \(F_n = [n, +\infty[\, \subset \mathbb{R}\). Show that each \(F_n\) is closed, that \(F_{n+1} \subset F_n\), and that \(\bigcap_{n \ge 0} F_n = \emptyset\).
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