On the rigid algebraic structure of Euclidean spaces

Abstract

It 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 Russian