Topological properties of prolongations and stable sets for semigroup actions - Rocha, Victor H. L. [UNESP]; Reis, Ronan A. [UNESP] (Elsevier B.V., 2021)
In this paper we study topological properties of Lyapunov stable sets for semigroup actions on Tychonoff spaces. We show that the stability and the asymptotical stability of a compact set is characterized by the stability and the asymptotical stability of its components, respectively. We also present a characterization of the stability of a compact set by means of omega-limit sets, prolongations, prolongational limit sets and the existence of a fundamental system of invariant neighborhoods of it. (c) 2021 Elsevier B.V. All rights reserved.
Keywords: Lyapunov stability; Asymptotical stability; Connected components; Prolongations; Semigroup actions