Some remarks about strong proximality of compact flows
Résumé
This note aims at providing some information about the concept of a strongly proximal set in a compact transformation semigroup. In the affine case, a unified approach of some know results are given. It is also pointed out that a compact flow $(X, S)$ is strong proximality if (and only) it is proximal and every point of $X$ has a strongly proximal neighborhood in $X$. The essential ingredient, in the affine as well as in the non-affine case, turns to be the existence of a unique minimal subset.