A characterization of $\ddot{I}‰$-limit sets in subshifts of Baire space

Abstract

In this paper we consider the structure of $\ddot{I}‰$-limit sets in subshifts of Baire space. We consider both subshifts of finite type and subshifts of bounded type and we demonstrate that many classical structure theorems for $\ddot{I}‰$-limit sets fail in this context. Nevertheless, we obtain characterizations of $\ddot{I}‰$-limit sets in subshift of finite types and of attracting $\ddot{I}‰$-limit sets in subshifts of bounded type.