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A direct solution to the Generic Point Problem

Author: Andy Zucker
Journal: Proc. Amer. Math. Soc. 146 (2018), 2143-2148
MSC (2010): Primary 37B05; Secondary 03E15
Published electronically: December 18, 2017
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Abstract: We provide a new proof of a recent theorem of Ben Yaacov,
Melleray, and Tsankov. If $ G$ is a Polish group and $ X$ is a minimal, metrizable $ G$-flow with all orbits meager, then the universal minimal flow $ M(G)$ is nonmetrizable. In particular, we show that given $ X$ as above, the universal highly proximal extension of $ X$ is nonmetrizable.

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Additional Information

Andy Zucker
Affiliation: Department of Mathematical Sciences, Carnegie Mellon University, 500 Forbes Avenue, Pittsburgh, Pennsylvania, 15213

Keywords: Topological dynamics, Baire category
Received by editor(s): April 29, 2017
Received by editor(s) in revised form: July 26, 2017, and July 27, 2017
Published electronically: December 18, 2017
Additional Notes: The author was partially supported by NSF Grant no. DGE 1252522.
Communicated by: Ken Ono
Article copyright: © Copyright 2017 American Mathematical Society

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