Escaping sets are not sigma-compact

Rempe, Lasse

doi:10.1090/proc/15576

Escaping sets are not sigma-compact
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by Lasse Rempe PDF

Proc. Amer. Math. Soc. 150 (2022), 171-177

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.

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