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 $\widehat{S}$.
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 $\widehat{S}$.
Classification :
54H15, 54H20
Keywords:
flow; dynamical system; left congruence; maximal group
Lawson, J. D.; Lisan, Amha T. Groups associated with minimal flows. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 2, pp. 471-477. http://geodesic.mathdoc.fr/item/CMJ_2005_55_2_a16/
@article{CMJ_2005_55_2_a16,
author = {Lawson, J. D. and Lisan, Amha T.},
title = {Groups associated with minimal flows},
journal = {Czechoslovak Mathematical Journal},
pages = {471--477},
year = {2005},
volume = {55},
number = {2},
mrnumber = {2137153},
zbl = {1081.54032},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMJ_2005_55_2_a16/}
}
TY - JOUR
AU - Lawson, J. D.
AU - Lisan, Amha T.
TI - Groups associated with minimal flows
JO - Czechoslovak Mathematical Journal
PY - 2005
SP - 471
EP - 477
VL - 55
IS - 2
UR - http://geodesic.mathdoc.fr/item/CMJ_2005_55_2_a16/
LA - en
ID - CMJ_2005_55_2_a16
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%A Lisan, Amha T.
%T Groups associated with minimal flows
%J Czechoslovak Mathematical Journal
%D 2005
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%N 2
%U http://geodesic.mathdoc.fr/item/CMJ_2005_55_2_a16/
%G en
%F CMJ_2005_55_2_a16
