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Transitive flows: a semi-group approach

Part of: Connections with other structures, applications

Published online by Cambridge University Press:  26 February 2010

J. D. Lawson  and
Amha Lisan
J. D. Lawson
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A.
Amha Lisan
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A.
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Abstract

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.

MSC classification

Secondary: 54H20: Topological dynamics

Information

Type
Research Article
Information
Mathematika , Volume 38 , Issue 2 , December 1991 , pp. 348 - 361
Copyright
Copyright © University College London 1991

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