English

Escaping sets are not sigma-compact

Dynamical Systems 2022-09-15 v4 Complex Variables General Topology

Abstract

Let ff be a transcendental entire function. The escaping set I(f)I(f) consists of those points that tend to infinity under iteration of ff. We show that I(f)I(f) is not σ\sigma-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

R2 v1 2026-06-23T16:44:37.453Z