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Transitive flows: a semi-group approach

  • J. D. Lawson (a1) and Amha Lisan (a1)

In this paper we characterize the universal pointed actions of a semigroup S on a compact space such that the orbit of the distinguished point is dense; such actions are called transitive. The characterization is given in terms of the universal right topological monoidal compactification of S. All transitive actions are shown to arise as quotients modulo left congruences on this universal compactification. Minimal actions are considered, and close connections between these and minimal left ideals of the compactification are derived.

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7. W. H. Gottschalk . Almost periodic points with respect to transformation semi-groups. Annals of Math., 47 (1946), 762766.

8. J. D. Lawson . Points of continuity for semigroup actions. Trans. Am. Math. Soc, 284 (1984), 183202.

9. W. A. F. Ruppert . Endomorphic actions of β(N) on the torus group. Semigroup Forum, 43 (1991), 202217.

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  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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