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On heredity of strongly proximal actions

C. R. E. Raja
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Abstract

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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C. R. E. Raja. 2003-03-28. On heredity of strongly proximal actions. https://arxiv.org/abs/math/0303361

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