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Filling analytic sets by the derivatives of  -smooth bumps |
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| Authors: | Mariá n Fabian Ondrej F K Kalenda Jan Kolá r |
| Institution: | Mathematical Institute, Czech Academy of Sciences, Zitná 25, 115 67 Praha 1, Czech Republic ; Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic ; Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic |
| Abstract: | If  is an infinite-dimensional Banach space, with separable dual, and  is an analytic set such that any point  can be reached from  by a continuous path contained (except for the point  ) in the interior of  , then  is the range of the derivative of a  -smooth function on  with bounded nonempty support. |
| Keywords: | $C^1$-smooth bump separable dual Banach space analytic set |
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