This note aims at providing some information about the concept of a strongly proximal compact transformation semigroup. In the affine case, a unified approach to some known results is given. It is also pointed out that a compact flow (X,𝓢) is strongly proximal if (and only if) it is proximal and every point of X has an 𝓢-strongly proximal neighborhood in X. An essential ingredient, in the affine as well as in the nonaffine case, turns out to be the existence of a unique minimal subset.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm115-2-2,
author = {A. Bouziad and J.-P. Troallic},
title = {Some remarks about strong proximality of compact flows},
journal = {Colloquium Mathematicae},
volume = {116},
year = {2009},
pages = {159-170},
zbl = {1177.54018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm115-2-2}
}
A. Bouziad; J.-P. Troallic. Some remarks about strong proximality of compact flows. Colloquium Mathematicae, Tome 116 (2009) pp. 159-170. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm115-2-2/