  We propose a definition of a quantum homogeneous space of a locally compact
quantum group. We show that classically it reduces to the notion of a
homogeneous spaces. On the quantum level our definition goes beyond the
quotient case. It provides a framework which, besides the Vaes' quotient of a
locally compact quantum group by its closed quantum subgroup (our main
motivation) is also compatible with, generically non-quotient, quantum
homogeneous spaces of a compact quantum group studied by P. Podles as well as
the Rieffel deformation of G-homogeneous spaces. Finally, our definition rules
out the paradoxical examples of the non-compact quantum homogeneous spaces of a
compact quantum group.
