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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A compact group which is not Valdivia compact
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by Wiesław Kubiś and Vladimir Uspenskij PDF
Proc. Amer. Math. Soc. 133 (2005), 2483-2487 Request permission

Abstract:

A compact space $K$ is Valdivia compact if it can be embedded in a Tikhonov cube $I^A$ in such a way that the intersection $K\cap \Sigma$ is dense in $K$, where $\Sigma$ is the sigma-product ($=$ the set of points with countably many non-zero coordinates). We show that there exists a compact connected Abelian group of weight $\omega _1$ which is not Valdivia compact, and deduce that Valdivia compact spaces are not preserved by open maps.
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Additional Information
  • Wiesław Kubiś
  • Affiliation: Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland
  • Email: kubis@ux2.math.us.edu.pl
  • Vladimir Uspenskij
  • Affiliation: Department of Mathematics, 321 Morton Hall, Ohio University, Athens, Ohio 45701
  • MR Author ID: 191555
  • Email: uspensk@math.ohiou.edu
  • Received by editor(s): November 1, 2003
  • Received by editor(s) in revised form: April 11, 2004
  • Published electronically: February 25, 2005
  • Communicated by: Alan Dow
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 2483-2487
  • MSC (2000): Primary 54D30; Secondary 54C15, 22C05
  • DOI: https://doi.org/10.1090/S0002-9939-05-07797-X
  • MathSciNet review: 2138892