Some remarks about strong proximality of compact flows
Volume 115 / 2009
Colloquium Mathematicum 115 (2009), 159-170
MSC: 54H20, 60B05.
DOI: 10.4064/cm115-2-2
Abstract
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 $(X, {\mathcal S})$ is strongly proximal if (and only if) it is proximal and every point of $X$ has an ${\mathcal S}$-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.
