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.References
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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