Escaping sets are not sigma-compact
Dynamical Systems
2022-09-15 v4 Complex Variables
General Topology
Abstract
Let be a transcendental entire function. The escaping set consists of those points that tend to infinity under iteration of . We show that is not -compact, resolving a question of Rippon from 2009.
Cite
@article{arxiv.2006.16946,
title = {Escaping sets are not sigma-compact},
author = {Lasse Rempe},
journal= {arXiv preprint arXiv:2006.16946},
year = {2022}
}
Comments
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