Nonmetrizable topological dynamical characterization of central sets

摘要

Without the restriction of metrizability, topological dynamical systems (X, (Ts)S￡C?) are defined and uniform recurrence and proximality are studied. Some well known results are generalized and some new results are obtained. In particular, a topolog-ical dynamical characterization of central sets in an arbitrary semigroup (G, +) is given and shown to be equivalent to the usual algebraic characterization.