Generalizations of expansiveness in Non-Autonomous Discrete Systems

In this paper, we define and study generalizations of expansiveness, namely n- expansiveness, ${\mathrm{\aleph }}_0$-expansiveness, continuum-wise expansive and meagre expansiveness for non-autonomous discrete dynamical systems. We discuss various properties of such non-autonomous systems and give necessary examples. We prove results related to non-existence of ${\mathrm{\aleph }}_0$-expansive and meagre expansive non-autonomous system on certain spaces. We also study relation between ${\mathrm{\aleph }}_0$-expansive and meagre-expansive non-autonomous systems.