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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.
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