Filling analytic sets by the derivatives of $C^1$-smooth bumps
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- by Marián Fabian, Ondřej F. K. Kalenda and Jan Kolář PDF
- Proc. Amer. Math. Soc. 133 (2005), 295-303 Request permission
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.References
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Additional Information
- Marián Fabian
- Affiliation: Mathematical Institute, Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic
- MR Author ID: 64760
- Email: fabian@math.cas.cz
- Ondřej F. K. Kalenda
- Affiliation: Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic
- ORCID: 0000-0003-4312-2166
- Email: kalenda@karlin.mff.cuni.cz
- Jan Kolář
- 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
- 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
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 295-303
- MSC (2000): Primary 54H05; Secondary 58C25, 46G05
- DOI: https://doi.org/10.1090/S0002-9939-04-07730-5
- MathSciNet review: 2086222