A characterization of submanifolds by a homogeneity condition (Q881458)

It is known that any smooth submanifold of a smooth manifold is smoothly ambient homogeneous. The goal of the paper under review is to prove the following theorem. Theorem: Let \(N\) be a locally compact subset of a smooth manifold \(M\). If \(N\) is smoothly ambient homogeneous then \(N\) is a smooth submanifold of \(M\).