Bounded-to-1 factors of an aperiodic shift of finite type are 1-to-1 almost everywhere factors also

We show that if: GHis a bounded-to-1 factor map from an irreducible shift of finite type Gwith period pG to a shift of finite type Hwith period pH, then there is a factor map that is (pG/pH)-to-1 almost everywhere. Moreover, if is right closing, then may be taken to be right closing also. © 1990, Cambridge University Press. All rights reserved.