Monotone decompositions into trees of Hausdorff continua irreducible about a finite subset

Irreducible Julia sets of rational functions

“…In this section, we review the notion of aposyndesis due to Jones [Jon41,Jon52] and an associated decomposition defined by Vought [Vou74]. The goal is to define a monotone map m : J(R) → Y , where Y is a topologically simpler space.…”

“…Theorem 8 (Theorem 1 of [Vou74]). Let M be a finished continuum which is irreducible about n points, but no fewer.…”