Topological mild mixing of all orders along polynomials

Yang Cao, Song Shao

A minimal system $(X,T)$ is topologically mildly mixing if all non-empty open subsets $U,V$, $\{n\in \mathbb{Z}:U\cap T^{-n}V\ne \varnothing \}$ is an IP${}^{\ast }$-set. In this paper we show that…