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A property of ![$ C_p[0,1]$](/tran/2011-363-05/S0002-9947-2010-05052-4/gif-title0/img1.gif)
Author:
Michael Levin
Journal:
Trans. Amer. Math. Soc. 363 (2011), 2295-2304
MSC (2000):
Primary 54C35, 54F45
Published electronically:
December 20, 2010
MathSciNet review:
2763717
Full-text PDF
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Additional Information
Abstract: We prove that for every finite-dimensional compact metric space  there is an open continuous linear surjection from ![$ C_p[0,1]$](/tran/2011-363-05/S0002-9947-2010-05052-4/gif-abstract0/img2.gif) onto  . The proof makes use of embeddings introduced by Kolmogorov and Sternfeld in connection with Hilbert's 13th problem.
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- 1.
- Kolmogorov, A. N. On the representation of continuous functions of many variables by superposition of continuous functions of one variable and addition. Amer. Math. Soc. Transl. (2) 28 (1963), 55-59. MR 0153799 (27:3760)
- 2.
- Ostrand, Phillip A. Dimension of metric spaces and Hilbert's problem
 . Bull. Amer. Math. Soc. 71 (1965), 619-622. MR 0177391 (31:1654)
- 3.
- Pavlovskiĭ, D. S. Spaces of continuous functions. Soviet Math. Dokl. 22 (1980), no. 1, 34-37 (1981). MR 577006 (82c:54014)
- 4.
- Sternfeld, Y. Superpositions of continuous functions. J. Approx. Theory 25 (1979), no. 4, 360-368. MR 535937 (82d:26008)
- 5.
- Sternfeld, Yaki. Hilbert's 13th problem and dimension. Geometric aspects of functional analysis (1987-88), 1-49, Lecture Notes in Math., 1376, Springer, Berlin, 1989. MR 1008715 (90j:54035)
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- Sternfeld, Yaki. Mappings in dendrites and dimension. Houston J. Math. 19 (1993), no. 3, 483-497. MR 1242434 (94j:54017)
- 7.
- Leiderman, Arkady; Morris, Sidney A.; Pestov, Vladimir The free abelian topological group and the free locally convex space on the unit interval. J. London Math. Soc. (2) 56 (1997), no. 3, 529-538. MR 1610463 (99a:22006)
- 8.
- Leiderman, A.; Levin, M.; Pestov, V. On linear continuous open surjections of the spaces
 . Topology Appl. 81 (1997), no. 3, 269-279. MR 1485772 (98j:54026)
- 9.
- Levin, Michael. Certain finite-dimensional maps and their application to hyperspaces. Israel J. Math. 105 (1998), 257-262. MR 1639771 (99g:54004)
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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:
http://dx.doi.org/10.1090/S0002-9947-2010-05052-4
PII:
S 0002-9947(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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