Filling analytic sets by the derivatives of 𝐶¹-smooth bumps

Fabian, Marián; Kalenda, Ondřej; Kolář, Jan

doi:10.1090/S0002-9939-04-07730-5

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.

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