2 problems

Let $(X,T)$ be a dynamical system with finite, nonzero mean dimension, meaning … Let $(Y,S)$ be a factor of $(X,T)$ via a factor map $\pi$, and write $\operatorname{mdim}(\pi,T)$ f…

Let $(X,T)$ be a dynamical system, and let $z\ne z'$ be distinct points of $X$. A factor of $(X,T)$ via a factor map $\pi$ is a dynamical system $(Y,S)$ with $\pi\colon X\to Y$ int…