Exercise 4, § 6

a) Every closed subspace of an exhaustible locally convex space is exhaustible. b) Let E be an exhaustible locally convex space, and $u : E \to F$ a continuous linear surjective mapping from E into F. Show that F is exhaustible. In particular, every quotient space of E by a closed subspace of E is exhaustible. Every space obtained by assigning to E a Hausdorff locally convex topology coarser than that of E is exhaustible.