Escaping endpoints always explode

Let $a\in \C$. The set $\tilde{E}(f_a)$ is the set of escaping endpoints associated with the parameter $a$.

Escaping endpoints always explode. The set $\tilde{E}(f_a)$ is totally separated, and hence $\infty$ is an explosion point of $\tilde{E}(f_a)\cup\{\infty\}$.

The preceding results establish connectedness of $\tilde{E}(f_a)\cup\{\infty\}$, while this assertion would give the complementary total-separation property for every parameter. The source indicates that the claim is expected to hold in general, but does not establish it; its validity is tied to difficult questions about accumulation of dynamical rays.