  The two main theorems of this paper provide a characterization of hyperbolic
affine iterated function systems defined on Rm. Atsushi Kameyama (Distances on
Topological Self-Similar Sets, Proceedings of Symposia in Pure Mathematics,
Volume 72.1, 2004) asked the following fundamental question: given a
topological self-similar set, does there exist an associated system of
contraction mappings? Our theorems imply an affirmative answer to Kameyama's
question for self-similar sets derived from affine transformations on Rm.
