# Article

Full entry | PDF   (0.3 MB)
Keywords:
flow; dynamical system; left congruence; maximal group
Summary:
Let \$S\$ be topological semigroup, we consider an appropriate semigroup compactification \$\widehat{S}\$ of \$S\$. In this paper we study the connection between subgroups of a maximal group in a minimal left ideal of \$\widehat{S}\$, which arise as equivalence classes of some closed left congruence, and the minimal flow characterized by the left congruence. A particular topology is defined on a maximal group and it is shown that a closed subgroup under this topology is precisely the intersection of an equivalence class with the maximal group for some left congruence on \$\widehat{S}\$.
References:
[1] J.  Auslander: Minimal Flows and Their Extensions. North-Holland, Amsterdam, 1988. MR 0956049 | Zbl 0654.54027
[2] J. E.  Berglund, H. D.  Junghenn and P.  Milnes: Analysis on Semigroups. John Wiley and Sons, New York, 1989. MR 0999922
[3] R. Ellis: Lectures on Topological Dynamics. Benjamin, New York, 1969. MR 0267561 | Zbl 0193.51502
[4] J. D. Lawson: Flows and compactifications. J. London Math. Soc. 46 (1992), 349–363. MR 1182489 | Zbl 0769.54045
[5] J. D. Lawson and Amha Lisan: Transitive flows: a semigroup approach. Mathematika 38 (1991), 348–361. DOI 10.1112/S0025579300006690 | MR 1147834
[6] J. D. Lawson and Amha Lisan: Flows, congruences, and factorizations. Topology Appl. 58 (1994), 35–46. DOI 10.1016/0166-8641(94)90072-8 | MR 1280709

Partner of