Locally contractive maps on perfect Polish ultrametric spaces

Abstract

In this paper, we present a result concerninglocally contractive maps defined on subsets of perfect Polishultrametric spaces (i.e. separable complete ultrametric spaces).Specifically, we show that a perfect compact ultrametric spacecannot be contained in its locally contractive image, a corollaryrelating this result to minimal dynamical systems, and pose aconjecture for the general Polish ultrametric case.