Structure of homogeneous locally compact spaces with intrinsic metric (Q909257)

The topological characteristic of a homogeneous locally compact space M with intrinsic metric \(\rho\) is given. Such a space is a manifold if and only if it is locally contractible. In the general case M is represented as a projective limit of a sequence of homogeneous manifolds \(M_ n\) with an intrinsic metric \(\rho_ n\).