Escaping sets are not sigma-compact

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.

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

References in corpus (1)

• The topological dimension of radial Julia sets

Cited by in corpus (1)

• Exponential iteration and Borel sets