Exercise 3, § 2

Let (I_n) be an infinite sequence of non-empty open intervals in R such that $\overline{I}_n \cap \overline{I}_m = \varnothing$ for m ≠ n. Show that the complement of the union of the I_n is a perfect set (Chapter I, § 2, no. 6); in particular, Cantor’s triadic set is perfect.