Locally Contractive Maps on Perfect Polish Ultrametric Spaces
Dynamical Systems
2015-05-04 v2 General Topology
Abstract
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.
Cite
@article{arxiv.1502.03538,
title = {Locally Contractive Maps on Perfect Polish Ultrametric Spaces},
author = {Francis George},
journal= {arXiv preprint arXiv:1502.03538},
year = {2015}
}
Comments
9 pages