Abstract
We generalize an important theorem of Fred Galvin from the Stone-Cech compactification βT of any discrete semigroup T to any compact Hausdorff right-topological semigroup with a dense topological center; and then apply it to Ellis’ semigroups to prove that a point is distal if and only if it is IP*-recurrent, for any semiflow (T;X) with arbitrary compact Hausdorff phase space X not necessarily metrizable and with arbitrary phase semigroup T not necessarily cancelable.
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