Exercise 7, § 4

a) Let A be a convex set with at least one interior point in a topological vector space E. Show that the set of internal points of A is identical with the interior of A (cf. exerc. 5, b)). b) Show that in the normed space $E = l^1(\mathbf{N})$, the convex cone P defined in II, p. 66, exerc. 11, b), generates E but does not contain any internal point.