Exercise 2, § 2

Give an example of two topological spaces T_1 and T_2 and a bijective continuous mapping f of T_1 onto T_2, such that the mapping $\mu \mapsto f(\mu)$ of $\mathscr{M}_+^b(T_1)$ into $\mathscr{M}_+^b(T_2)$ is not surjective.