Mathematika

Research Article

Transitive flows: a semi-group approach

J. D. Lawsona1 and Amha Lisana2

a1 Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A.

a2 Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A.

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.

(Received February 01 1991)

Key Words:

  • 54H20: GENERAL TOPOLOGY; Connections with other structures, applications; Topological dynamics.