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Space-times which allow a slicing into homogeneous spatial hypersurfacesgeneralize the usual Bianchi models. One knows already that in these models theBianchi type may change with time. Here we show which of the changes reallyappear. To this end we characterize the topological space whose points are the3-dimensional oriented homogeneous Riemannian manifolds; locally isometricmanifolds are considered as same.Comment: 28 pages, Late

Inhomogeneous cosmological models with homogeneous inner hypersurface geometry