A characterization of submanifolds by a homogeneity condition

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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

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Geometric Topology, Differential Geometry, 57R50; 58A05; 53A04; 54H11

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http://salesiana.dossiersoluciones.com/handle/123456789/131098

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0606470
 http://arxiv.org/abs/math/0606470
 Topol. Appl. 154 (2007) 1894-1897
 doi:10.1016/j.topol.2007.03.002

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arXiv