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Science China Mathematics

, Volume 60, Issue 12, pp 2421–2428 | Cite as

On Galvin’s theorem for compact Hausdorff right-topological semigroups with dense topological centers

  • XiongPing DaiEmail author
  • HaiLan Liang
Articles

Abstract

We generalize an important theorem of Fred Galvin from the Stone-Čech 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.

Keywords

Galvin’s theorem transformation semigroup Ellis’ semigroup distal point 

MSC(2010)

37B05 20M30 54H15 

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of MathematicsNanjing UniversityNanjingChina
  2. 2.Department of MathematicsFuzhou UniversityFuzhouChina

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