An extension theorem for closing maps of shifts of finite type

If there exists some right-closing factor map π: ΣA → ΣB between aperiodic shifts of finite type, then any right-closing map φ → ΣBfrom any shift of finite type X contained in ΣA can be extended to a right-closing factor map from all of ΣA onto ΣB We prove this and give some consequences. © 1993 American Mathematical Society.