2 problems

For a topological dynamical system $(X,T)$, let $\textbf{AP}^{[2]}(X,T)$ denote its order-two approximate proximal relation and let $\Delta_X=\\{(x,x):x\in X\\}$. Approximate-proxi…

Let $(X,T)$ be a minimal distal system. The arithmetic-progression proximality conjecture. … Here ${\bf AP}^{[d]}$ denotes the regionally proximal relation of order $d$ along arith…