Exercise 5, § 2

Let K be a Hausdorff topological division ring of which the topology is locally retrobounded (GT, III, § 6, exerc. 22). Extend prop. 2 of I, p. 12 and th. 1 of I, p. 13 to topological vector spaces over K ; similarly extend th. 2 of I, p. 13 and prop. 3 of I, p. 14 when K is also complete.