Proximal and syndetical properties in nonautonomous discrete systems

This paper is mainly concerned with a class of nonautonomous discrete systems $(X, f_{1,\infty})$. New definitions of proximity relations and sensitivity in nonautonomous discrete systems are given. Some relations among $P(f_{1,\infty})$, $L(f_{1,\infty})$, $R(f_{1,\infty})$, $S(f_{1,\infty})$ and $P(f_{1,\infty})(x)$ are derived. And some chaotic properties of $f_{1,\infty}$ are proved.