Sliding block codes between shift spaces over infinite alphabets

Recently Ott, Tomforde and Willis introduced a notion of one-sided shifts over infinite alphabets and proposed a definition for sliding block codes between such shift spaces. In this work we propose a more general definition for sliding block codes between Ott–Tomforde–Willis shift spaces and then we prove Curtis–Hedlund–Lyndon type theorems for them, finding sufficient and necessary conditions under which the class of the sliding block codes coincides with the class of continuous shift-commuting maps