Exercise 1, § 5

Let I be an uncountable set, and let E be the space R^{(I)} endowed with the topology defined in I, p. 24, exerc. 14; let E' be its dual (IV, p. 50, exerc. 16, c)). Show that in E' there exist non relatively compact (for σ(E', E)) subsets H such that from every sequence of points of H we can extract a sequence which converges to a point of H for σ(E', E).