Exercise 1, § 3

Let $E$ be a locally convex metrizable space, and $E'_b$ its strong dual. If $E'_b$ is metrizable, prove that the topology of $E$ can be defined by a single norm (use III, p. 37, exerc. 2 and p. 38, exerc. 5 and also the fact that $E$ is bornological).