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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Filling analytic sets by the derivatives of $C^1$-smooth bumps


Authors: Marián Fabian, Ondrej F. K. Kalenda and Jan Kolár
Journal: Proc. Amer. Math. Soc. 133 (2005), 295-303
MSC (2000): Primary 54H05; Secondary 58C25, 46G05
Published electronically: August 24, 2004
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Abstract | References | Similar Articles | Additional Information

Abstract: If $X$ is an infinite-dimensional Banach space, with separable dual, and $M\subset X^*$ is an analytic set such that any point $x^*\in M$ can be reached from $0$ by a continuous path contained (except for the point $x^*$) in the interior of $M$, then $M$ is the range of the derivative of a $C^1$-smooth function on $X$ with bounded nonempty support.


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Additional Information

Marián Fabian
Affiliation: Mathematical Institute, Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic
Email: fabian@math.cas.cz

Ondrej F. K. Kalenda
Affiliation: Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic
Email: kalenda@karlin.mff.cuni.cz

Jan Kolár
Affiliation: Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic
Email: kolar@karlin.mff.cuni.cz

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07730-5
PII: S 0002-9939(04)07730-5
Keywords: $C^1$-smooth bump, separable dual Banach space, analytic set
Received by editor(s): March 21, 2002
Published electronically: August 24, 2004
Additional Notes: The first author’s research was supported by grants A101 90 03, A101 93 01 and GA ČR 201/01/1198.
The second author’s research was supported by grants GAUK 277/2001, MSM 113200007 and GA ČR 201/00/1466
The third author’s research was supported by grants MSM 113200007 and GA ČR 201/02/D111
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.