A characterization of submanifolds by a homogeneity condition
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 Uy such that h(x)=y and h (Ux N) = Uy N. Then N is a smooth submanifold of M.
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