Expansive Homeomorphisms on non-Hausdorff Spaces

TL;DR

This paper explores expansive dynamical systems on non-Hausdorff spaces, extending classical concepts to broader topological contexts and analyzing their properties and examples.

Contribution

It introduces orbit and refinement expansivity for non-Hausdorff spaces, expanding the scope of expansive dynamics beyond metric spaces.

Findings

Examples of expansive systems on non-Hausdorff compact spaces

Relations between expansivity and topological properties like separability and metrizability

Analysis of uniform expansivity in non-Hausdorff settings

Abstract

We study expansive dynamical systems from the viewpoint of general topology. We introduce the notions of orbit and refinement expansivity on topological spaces extending expansivity in the compact metric setting. Examples are given on non-Hausdorff compact spaces. Topological properties are studied in relation to separability axioms, metrizability and uniform expansivity.