# Generalizations of expansiveness in Non-Autonomous Discrete Systems

## TL;DR

This paper introduces and analyzes new generalizations of expansiveness in non-autonomous discrete dynamical systems, exploring their properties, examples, and limitations on certain spaces.

## Contribution

It defines several new types of expansiveness for non-autonomous systems and investigates their properties and non-existence results.

## Key findings

- Non-existence of $\u2205_0$-expansive systems on certain spaces
- Non-existence of meagre expansive systems on certain spaces
- Relations between different generalized expansiveness concepts

## Abstract

In this paper, we define and study generalizations of expansiveness, namely n- expansiveness, $\aleph_0$-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 $\aleph_0$-expansive and meagre expansive non-autonomous system on certain spaces. We also study relation between $\aleph_0$-expansive and meagre-expansive non-autonomous systems.