Partial semigroup partial dynamical systems and Partial Central Sets

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-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 \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.