3 problems

Let $(X,T)$ be a subshift. Call $(X,T)$ irreducible if, for every pair of finite words $u,v$ occurring in points of $X$, some finite word $w$ occurs in a point of $X$ such that…

Let $(X,T)$ be a rank-one subshift with bounded spacer parameter, and suppose that $(Y,S)$ is a factor of $(X,T)$. Bounded-spacer factor-isomorphism conjecture. Either $Y$ is finit…

Let $(X,T)$ be a rank-one subshift and let $(Y,S)$ be a topological factor of $(X,T)$. A topological factor is a dynamical system equipped with a continuous factor map intertwining…