Topological properties of prolongations and stable sets for semigroup actions
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Elsevier B.V.
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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.
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Lyapunov stability, Asymptotical stability, Connected components, Prolongations, Semigroup actions
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Inglês
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Topology And Its Applications. Amsterdam: Elsevier, v. 291, 22 p., 2021.
