Escaping sets of continuous functions

Ian Short; David J. Sixsmith

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arXiv · 1601.04010

Escaping sets of continuous functions

Ian Short·David J. Sixsmith

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Abstract

Our objective is to determine which subsets of $\mathbb{R}^d$ arise as escaping sets of continuous functions from $\mathbb{R}^d$ to itself. We obtain partial answers to this problem, particularly in one dimension, and in the case of open sets. We give a number of examples to show that the situation in one dimension is quite different from the situation in higher dimensions. Our results demonstrate that this problem is both interesting and perhaps surprisingly complicated.

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Ian Short, David J. Sixsmith. 2016-01-15. Escaping sets of continuous functions. https://arxiv.org/abs/1601.04010

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