The induced contractive maps on the covering spaces

‎ ‎Let (\tilde{X},p) be the universal covering space of a compact metrizable space X ‎, ‎which is compact and locally path connected‎. ‎In this paper‎, ‎we show that there exist metrics d and d' for X and \tilde{X} ‎, ‎respectively‎, ‎such that any contractive map ‎ f:X\to X induces a contractive map on \tilde{X}. ‎As an‎ application‎, ‎it is obtained that every iterated function system(IFS) on the space X with attractor K ‎, ‎induces an IFS on \tilde{ X} with attractor \tilde{K}, such that p(\tilde{K})=K‎.

Keywords:

Covering spaces‎ , ‎Iterated function systems‎ , ‎Contractive maps