On estimations of the generalized Hausdorff dimension (Q2212397)

The authors introduce the abstract concept of a homogeneous dimensional space and associate with such spaces a finite compactness index. Additionally, they define a Hausdorff-Besicovitch dimension spectrum and prove a theorem about the values of the Hausdorff-Besicovitch dimension spectrum for subspaces of homogenous dimensional spaces. Estimates for the dimension of sets generated by contractive mappings are also given. These estimates are an abstract version of the Douady-Oesterle theorem on the dimension of attractors for smooth dynamical systems in Euclidean spaces.