Escaping sets of continuous functions

Short, Ian and Sixsmith, David J. (2019). Escaping sets of continuous functions. Journal d'Analyse Mathematique, 137(2) pp. 875–869.

DOI: https://doi.org/10.1007/s11854-019-0015-9

Abstract

Our objective is to determine which subsets of R^d arise as escaping sets of continuous functions from 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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About

• Item ORO ID
• 45214
• Item Type
• Journal Item
• ISSN
• 1565-8538
• Project Funding Details

• Funded Project Name	Project ID	Funding Body
  Not Set	Not Set	The Open University (OU)
  Not Set	EP/L019841/1	Engineering and Physical Sciences Research Council

• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2019 The Hebrew University of Jerusalem
• Related URLs
• • https://arxiv.org/abs/1601.04010(Other)
  • https://rdcu.be/brUTN
• Depositing User
• Ian Short