INFINITE INTEGRATED FUNCTION SYSTEMS

We examine iterated function systems consisting of a countably infinit e number of contracting mappings (IIFS). We state results analogous to the well-known case of finitely many mappings (IFS). Moreover, we sho w that IIFS can be approximated by appropriately chosen IFS both in te rms of Hausdorff distance and of Hausdorff dimension. Comparing the de scriptive power of IFS and IIFS as mechanisms defining closed and boun ded sets, we show that IIFS are strictly more powerful than IFS. On th e other hand, there are closed and bounded non-empty sets not describa ble by IIFS.