A RELATIONSHIP BETWEEN PACKING AND TOPOLOGICAL DIMENSIONS

The relationship between the topological dimension of a separable metr ic space and the Hausdorff dimensions of its homeomorphic images has b een known for some time. In this note we consider topological and pack ing dimensions, and show that if X is a separable metric space, then d im(T) (X) = min {dim(P) (X') : X' is homeomorphic to X}, where dim(T) (X) and dim(P) (X) denote the topological and packing dimensions of X, respectively.