Exercise 2, § 2

$a$) Show that every product of infra-barrelled spaces is infra-barrelled. (Reduce to the case of Hausdorff infra-barrelled spaces; then use exerc. 1 and prop. 15 of IV, p. 14.) b) Give an example of a Hausdorff and infra-barrelled locally convex space which is neither bornological non barrelled. (Proceed as in III, p. 45, exerc. 16, replacing the barrelled spaces by infra-barrelled spaces and use $a$.)