# Topological characteristic factors and independence along arithmetic progressions

25 Feb 2020 Cai Fangzhou Shao Song

Let $\pi: (X,T)\rightarrow (Y,T)$ be a factor map of topological dynamics and $d\in {\mathbb {N}}$. $(Y,T)$ is said to be a $d$-step topological characteristic factor if there exists a dense $G_\delta$ set $X_0$ of $X$ such that for each $x\in X_0$ the orbit closure $\overline{\mathcal O}((x, \ldots,x), T\times T^2\times \ldots \times T^d)$ is $\pi\times \ldots \times \pi$ ($d$ times) saturated... (read more)

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