A property of
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
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We prove that for every finite-dimensional compact metric space there is an open continuous linear surjection from
onto
. The proof makes use of embeddings introduced by Kolmogorov and Sternfeld in connection with Hilbert's 13th problem.
- 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)
- 6. 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)
Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 54C35, 54F45
Retrieve articles in all journals with MSC (2000): 54C35, 54F45
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.