Topology of global attractors for homeomorphisms with the topological shadowing property in ${\mathbb{R}}^m$

This paper studies the behavior of dynamical systems in non-compact spaces, specifically focusing on the concepts of global attractors and shadowing. Let $K$ be a compact global attractor. We show that the shadowing property holds in certain types of dynamical systems in non-compact spaces if and only if $K$ is trivial.