Locally contractive maps on perfect Polish ultrametric spaces. (English) Zbl 1461.37015

Summary: In this paper we present a result concerning locally contractive maps defined on subsets of perfect Polish ultrametric spaces (i.e. separable complete ultrametric spaces). Specifically, we show that a perfect compact ultrametric space cannot be contained in its locally contractive image, a corollary relating this result to minimal dynamical systems, and pose a conjecture for the general Polish ultrametric case.


37B02 Dynamics in general topological spaces
37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
Full Text: arXiv EMIS