2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131098A 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 correctedGeometric TopologyDifferential Geometry57R50; 58A05; 53A04; 54H11text