Class-Closing Factor Codes and Constant-Class-To-One Factor Codes from Shifts of Finite Type

We define class-closing factor codes from shifts of finite type and show that they are continuing if their domains are irreducible and their images are of finite type. We establish several relations between class-closing factor codes, continuing factor codes and constant-class-to-one factor codes. In particular it is shown that a factor code between irreducible shifts of finite type is constant-class-to-one if and only if it is bi-class-closing, generalizing a result of Nasu.