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Nonmetrizable topological dynamical characterization of central sets

Hong-Ting Shi, Hong-Wei Yang (1996)

Fundamenta Mathematicae

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

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