MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Locally contractive maps on perfect Polish ultrametric spaces
Francis George

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.

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Keywords: contractive map; Polish space; ultrametric space, R-tree; dynamical system.

MSC: 37B05, 54H20, 54E40

Pages:  233--240     

Volume  68 ,  Issue  4 ,  2016