One-sided shift spaces over innite alphabets
William Ott, Mark Tomforde, Paulette N. Willis · arXiv (Cornell University) · 2014
We dene a notion of (one-sided) shift spaces over innite alphabets. Unlike many previous approaches to shift spaces over count- able alphabets, our shift spaces are compact Hausdor spaces. We ex- amine shift morphisms between these shift spaces, and identify three distinct classes that generalize the shifts of nite type. We show that when our shift spaces satisfy a property that we call \row-nite, shift morphisms on them may be identied with sliding block codes. As ap- plications, we show that if two (possibly innite) directed graphs have edge shifts that are conjugate, then the groupoids of the graphs are isomorphic, and the C -algebras of the graphs are isomorphic.