Abstract
It is well known that n-dimensional spaces of constant curvature (that is, hyperbolic, Euclidean, elliptic and spherical spaces) have (n -+ 1)n/2-dimensional continuous groups of motions. All the other n-dimensional geometric formations that up to now are known admit lesser freedom of motion.1 It seems natural to pose the problem of characterizing spaces of constant curvature as the only type of topological spaces with a sufficient amount of freedom of motion. To this end, we consider a topological space R and a group F of single-valued continuous mappings of R onto itself. To make F similar to a group of motions, it is natural to require that elements of F be uniformly equicontinuous.2
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