Exercise 5, § 10

Let $f : X \to Y$ be a proper mapping. a) Show that if $X$ is regular then $f(X)$ is a regular subspace of $Y$. b) Show that if $f(X)$ is a Lindelöf subspace of $Y$ ($§ 9$, Exercise 14), then $X$ is Lindelöf (use Proposition 10 of § 5, no. 4).