Exercise 23, § 4

a) Every regular Lindelöf space (Chapter I, § 9, Exercise 15) is paracompact [use Exercise 20 a)].

b) The product of a Lindelöf space and a compact space is a Lindelöf space (argue as in the proof of Proposition 17 of Chapter I, § 9, no. 10; cf. § 5, Exercise 16).