Rocha, Victor H. L. [UNESP]Reis, Ronan A. [UNESP]2021-06-252021-06-252021-03-15Topology And Its Applications. Amsterdam: Elsevier, v. 291, 22 p., 2021.0166-8641http://hdl.handle.net/11449/210077In 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.22engLyapunov stabilityAsymptotical stabilityConnected componentsProlongationsSemigroup actionsArtigo10.1016/j.topol.2021.107611WOS:000623100400006