2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59251It is shown that the groups of automorphisms of Euclidean spaces are isomorphic to the groups of topologic automorphisms of respectively factored arithmetic spaces. In particular, the geometry of Euclidean n-space with positive signature is associated with factorization of n-dimensional arithmetic space into n-dimensional sphere.PostScript, 6 pages, 6 figures, in RussianGeneral Mathematicstext