On heredity of strongly proximal actions

Details On heredity of strongly proximal actions On heredity of strongly proximal actions

2003-03-28

arxiv.org/abs/math/0303361v1

Archivum Math. (Brno) 39 (2003), 51-55.

Mathematics

Dynamical Systems

6pages. to appear in Archivum Math. (Brno) (2003)

Scientific paper

We prove that action of a semigroup T on compact metric space X by continuous selfmaps is strongly proximal if and only if T action on P(X), the space of probability measures on $X$ with weak topology, is strongly proximal. As a consequence we prove that affine actions on certain compact convex subsets of finite-dimensional vector spaces are strongly proximal if and only if the action is proximal.

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