Groups associated with minimal flows

, 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

\hat{S}

.

How to cite

top

MLA
BibTeX
RIS

Lawson, J. D., and Lisan, Amha T.. "Groups associated with minimal flows." Czechoslovak Mathematical Journal 55.2 (2005): 471-477. <http://eudml.org/doc/30960>.

@article{Lawson2005,
abstract = {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 $\widehat\{S\}$.},
author = {Lawson, J. D., Lisan, Amha T.},
journal = {Czechoslovak Mathematical Journal},
keywords = {flow; dynamical system; left congruence; maximal group; flow; dynamical system; left congruence; maximal group},
language = {eng},
number = {2},
pages = {471-477},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Groups associated with minimal flows},
url = {http://eudml.org/doc/30960},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Lawson, J. D.
AU - Lisan, Amha T.
TI - Groups associated with minimal flows
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 2
SP - 471
EP - 477
AB - 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 $\widehat{S}$.
LA - eng
KW - flow; dynamical system; left congruence; maximal group; flow; dynamical system; left congruence; maximal group
UR - http://eudml.org/doc/30960
ER -

References

top

Minimal Flows and Their Extensions, North-Holland, Amsterdam, 1988. (1988) Zbl0654.54027 MR0956049
Analysis on Semigroups, John Wiley and Sons, New York, 1989. (1989) MR0999922
Lectures on Topological Dynamics, Benjamin, New York, 1969. (1969) Zbl0193.51502 MR0267561
Flows and compactifications, J. London Math. Soc. 46 (1992), 349–363. (1992) Zbl0769.54045 MR1182489
10.1112/S0025579300006690, Mathematika 38 (1991), 348–361. (1991) MR1147834 DOI10.1112/S0025579300006690
10.1016/0166-8641(94)90072-8, Topology Appl. 58 (1994), 35–46. (1994) MR1280709 DOI10.1016/0166-8641(94)90072-8

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Language to use for this widget.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Number of notes per page

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.