Global attractors for semigroup actions on uniformizable spaces

TL;DR

This paper extends the concept of global attractors from metric spaces to uniformizable spaces for semigroup actions, providing conditions for their existence and exploring their relationship with global uniform attractors.

Contribution

It introduces a generalized framework for global attractors in uniformizable spaces and analyzes their properties and existence conditions.

Findings

Conditions for the existence of global attractors are established.

Relationship between global attractors and global uniform attractors is clarified.

Extension of attractor theory to broader topological spaces is demonstrated.

Abstract

In this paper the notion of global attractor is extended from the setting of semigroup actions on metric spaces to the setting of semigroup actions on uniformizable spaces. General conditions for the existence of global attractor are discussed and its relationship with the global uniform attractor is presented.