on the rank problem for factors of cantor minimal systems

A cantor minimal system is called of finite topological rank if it has a bratteli-vershik representation whose number of vertices per level is uniformly bounded. we prove that if the topological rank of a cantor minimal system is finite then all its minimal cantor factors have finite topological rank as well. this gives an affirmative answer to an open question posed by donoso, durand, maass, and petite in full generality.as a consequence, we obtain the dichotomy of downarowicz and maassfor cantor factors of finite rank cantor minimal systems: they are either odometers or subshifts.