Completely invariant closed set of a rational map
= Completely invariant closed set of a rational map
If a closed set $E$ satisfies $f^{-1}(E)=E$ for a rational map of degree at least two, then either $E$ has at most two points and lies in the <Fatou set>, or $J(f)\subseteq E$. The complement omits every point of $E$, so <Montel theorem> proves normality when $|E|\geq3$.