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Separating Points of βℕ By Minimal Flows

Published online by Cambridge University Press:  20 November 2018

Neil Hindman ,
Jimmie Lawson  and
Amha Lisan
Neil Hindman
Affiliation:
Department of Mathematics, Howard University Washington, D. C. 20059, U.S.A.
Jimmie Lawson
Affiliation:
Department of Mathematics, Louisiana State University Baton Rouge, Louisiana 70803, U.S.A.
Amha Lisan
Affiliation:
Department of Mathematics, Louisiana State University Baton Rouge, Louisiana 70803, U.S.A.
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Abstract

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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 .

Keywords

22A30
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 4 , 01 August 1994 , pp. 758 - 771
Copyright
Copyright © Canadian Mathematical Society 1994

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