  Space-times which allow a slicing into homogeneous spatial hypersurfaces
generalize the usual Bianchi models. One knows already that in these models the
Bianchi type may change with time. Here we show which of the changes really
appear. To this end we characterize the topological space whose points are the
3-dimensional oriented homogeneous Riemannian manifolds; locally isometric
manifolds are considered as same.
