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2 results

  • Separating Points of βℕ By Minimal Flows

  • Neil Hindman, Jimmie Lawson, Amha Lisan
  • Journal:
    Canadian Journal of Mathematics / Volume 46 / Issue 4 / 01 August 1994
    Published online by Cambridge University Press:
    20 November 2018, pp. 758-771
    Print publication:
    01 August 1994
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  • We consider minimal left ideals L of the universal semigroup compactification of a topological semigroup S. We show that the enveloping semigroup of L is homeomorphically isomorphic to if and only if given q ≠ r in , there is some p in the smallest ideal of with qp ≠ rp. We derive several conditions, some involving minimal flows, which are equivalent to the ability to separate q and r in this fashion, and then specialize to the case that S = , and the compactification is . Included is the statement that some set A whose characteristic function is uniformly recurrent has .

  • Transitive flows: a semi-group approach

  • Part of
  • J. D. Lawson, Amha Lisan
  • Journal:
    Mathematika / Volume 38 / Issue 2 / December 1991
    Published online by Cambridge University Press:
    26 February 2010, pp. 348-361
    Print publication:
    December 1991

  • 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.