2024/06/07 by H. Goodarzi, Goodarzi, H., M. Akbari Tootkaboni +3
Computer Science · Mathematics · #05D10 #2020 MSC: 37B02 #22A15 #22A15 Secondary: 05D10. 37B02 #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Dynamics and Fractals #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2406.04672
openalex publication_date 2024/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
H. Furstenberg defined Central sets in ℕ by using the notions of topological dynamics, later Bergelson and Hindman characterized central sets in ℕ and also in arbitrary semigroup in terms of algebra of Stone-Čech compactification of that set. We state the new notion of large sets in a partial semigroup setting and characterize the algebraic structure of the sets by using the algebra of Stone-Čech compactification. By using these notions, we introduce the Partial Semigroup Partial Dynamical System(PSPDS) and show that topological dynamical characterization of central sets in a partial semigroup is equivalent to the usual algebraic characterization.