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Escaping sets are not sigma-compact

Published 30 Jun 2020 in math.DS, math.CV, and math.GN | (2006.16946v4)

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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