  In this paper we revisit the theory of induced representations in the setting
of locally compact quantum groups. In the case of induction from open quantum
subgroups, we show that constructions of Kustermans and Vaes are equivalent to
the classical, and much simpler, construction of Rieffel. We also prove in
general setting the continuity of induction in the sense of Vaes with respect
to weak containment.
