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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Regular PI metric flows are equicontinuous


Author: Eli Glasner
Journal: Proc. Amer. Math. Soc. 114 (1992), 269-277
MSC: Primary 54H20
DOI: https://doi.org/10.1090/S0002-9939-1992-1070517-3
MathSciNet review: 1070517
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Abstract: Let $ (X,T)$ be a metrizable minimal flow. We show that a homomorphism $ X\mathop \to \limits^\pi Y$, which is regular, and PI can be decomposed as $ X\mathop \to \limits^\sigma Z\mathop \to \limits^\rho Y,\pi = \rho \circ \sigma $, where $ \rho $ is proximal and $ \sigma $ is a compact group extension. In particular, assuming further that $ T$ is abelian and taking $ Y$ to be the trivial one point flow, we find that a metric regular PI flow is a compact group rotation.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1070517-3
Article copyright: © Copyright 1992 American Mathematical Society