Partial semigroup partial dynamical systems and Partial Central Sets

Abstract

H. Furstenberg defined Central sets in $\mathbb{N}$ by using the notions of topological dynamics, later Bergelson and Hindman characterized central sets in $\mathbb{N}$ and also in arbitrary semigroup in terms of algebra of Stone-\v{C}ech 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-\v{C}ech compactification. By using these notions, we introduce the \emph{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.