ESCAPING SETS ARE NOT SIGMA-COMPACT



Rempe, Lasse ORCID: 0000-0001-8032-8580
(2022) ESCAPING SETS ARE NOT SIGMA-COMPACT. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 150 (1). pp. 171-177.

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Abstract

Let $f$ be a transcendental entire function. The escaping set $I(f)$ consists of those points that tend to infinity under iteration of $f$. We show that $I(f)$ is not $\sigma$-compact, resolving a question of Rippon from 2009.

Item Type: Article
Additional Information: 6 pages. To appear in Proc. Amer. Math. Soc. V4: Author accepted manuscript. Clarification of an imprecise statement regarding nowhere density in Corollary 2.2 that was present in v3
Uncontrolled Keywords: math.DS, math.DS, math.CV, math.GN, Primary 30D05, Secondary 37F10, 54D45
Depositing User: Symplectic Admin
Date Deposited: 16 Sep 2020 10:17
Last Modified: 15 Mar 2024 05:05
DOI: 10.1090/proc/15576
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3101280