Journal d'Analyse Mathématique

, Volume 137, Issue 2, pp 875–896 | Cite as

Escaping sets of continuous functions

  • Ian Short
  • David J. SixsmithEmail author


Our objective is to determine which subsets of ℝd arise as escaping sets of continuous functions from ℝd 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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Copyright information

© The Hebrew University of Jerusalem 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsThe Open UniversityMilton KeynesUK
  2. 2.School of Mathematical SciencesUniversity of NottinghamNottinghamUK

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