One-sided shift spaces over infinite alphabets

Abstract. We define a notion of (one-sided) shift spaces over infinite alphabets. Unlike many previous approaches to shift spaces over count-able alphabets, our shift spaces are compact Hausdorff spaces. We ex-amine shift morphisms between these shift spaces, and identify three distinct classes that generalize the shifts of finite type. We show that when our shift spaces satisfy a property that we call “row-finite”, shift morphisms on them may be identified with sliding block codes. As ap-plications, we show that if two (possibly infinite) directed graphs have edge shifts that are conjugate, then the groupoids of the graphs ar