A characterization of submanifolds by a homogeneity condition
arXiv:math/0606470 · doi:10.1016/j.topol.2007.03.002
Abstract
A very short proof of the following smooth homogeneity theorem of D. Repovs, E. V. Scepin and the author is presented. Let N be a locally compact subset of a smooth manifold M. Assume that for each two points x,y in N there exist their neighborhoods Ux and Uy in M and a diffeomorphism h : Ux \to Uy such that h(x)=y and h (Ux \cap N) = Uy \cap N. Then N is a smooth submanifold of M.
4 pages, meaning-distorting typos corrected