Bourbaki

Exercise 12, § 5

General Topology, IV, 391

Let (un)(u_n) be a sequence of real numbers >0> 0 such that

lim inf⁡n→∞un=0. \liminf_{n \to \infty} u_n = 0.
Show that there is an infinite number of indices nn such that un≤umu_n \leq u_m for all m≤nm \leq n.

Solution

No solution has been written yet.

Transcribed from the printed volume. Not translated.