An extension theorem for closing maps of shifts of finite type

Abstract

If there exists some right-closing factor map π : Σ A → Σ B \pi :{\Sigma _A} \to {\Sigma _B} between aperiodic shifts of finite type, then any right-closing map φ : X → Σ B \varphi :X \to {\Sigma _B} from any shift of finite type X X contained in Σ A {\Sigma _A} can be extended to a right-closing factor map from all of Σ A {\Sigma _A} onto Σ B {\Sigma _B} . We prove this and give some consequences.