3 problems

Let $(X,\mathcal B)$ be a standard Borel space, let $Aut(X,\mathcal B)$ denote its automorphism group equipped with the topology $p$, and let $\mathcal Sm$ be the class of smooth a…

Let $(Y,S)$ be a subshift with a collection $\mathcal C$ having property $F$ and entropy $h(\mathcal C)$. Let $(X,T)$ be a free Borel $\mathbb{Z}^d$ system, and write its Gurevic e…

Extension conjecture. There exists a smooth equivalence $\xi: \Omega_{1} \to \Omega_{2}$ that extends $\zeta$. This would establish the possibility of extending orbit equivalences…