Distinguishing endpoint sets from Erdős space

David S. Lipham

Published 2020-06-08Version 1

We show that the set of all escaping endpoints of the Julia set of $\exp(z)-1$ is not homeomorphic to $\mathbb Q \times X$ for any space $X$. In particular, it is not homeomorphic to Erd\H{o}s space $\mathfrak E$. Our proof demonstrates that the complement of the escaping endpoint set in $\mathbb C$ is path-connected.