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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.

Some remarks about strong proximality of compact flows