A GLUING LEMMA FOR ITERATED FUNCTION SYSTEMS

We obtain a special version of gluing lemma related to the theory of iterated function systems (IFS). As an application, we verify that a family of concrete n-dimensional self-affine tiles {Tn, r : 0 ≤ r < 3, n ≥ 3} are homeomorphic with the unit cube [0,1]n. The tiles Tn, r are "nontrivial" in the sense that each of them is neither a self-affine polytope nor the product of an interval with an (n - 1)-dimensional self-affine tile.