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A property of $ C_p[0,1]$


Author: Michael Levin
Journal: Trans. Amer. Math. Soc. 363 (2011), 2295-2304
MSC (2000): Primary 54C35, 54F45
DOI: https://doi.org/10.1090/S0002-9947-2010-05052-4
Published electronically: December 20, 2010
MathSciNet review: 2763717
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that for every finite-dimensional compact metric space $ X$ there is an open continuous linear surjection from $ C_p[0,1]$ onto $ C_p(X)$. The proof makes use of embeddings introduced by Kolmogorov and Sternfeld in connection with Hilbert's 13th problem.

References [Enhancements On Off] (What's this?)

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Additional Information

Michael Levin
Affiliation: Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, Be’er Sheva 84105, Israel
Email: mlevine@math.bgu.ac.il

DOI: https://doi.org/10.1090/S0002-9947-2010-05052-4
Keywords: $C_{p}$-spaces, basic embeddings
Received by editor(s): June 18, 2008
Published electronically: December 20, 2010
Additional Notes: The author was supported by ISF grant 836/08
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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