Filling analytic sets by the derivatives of C1-smooth bumps

Abstrakt

If X is an infinite-dimensional Banach space, with separable dual, and M is an analytic subset of X* such that any point can be reached from 0 by a continuous path contained (except for the point itself) in the interior of M, then M is the range of the derivative of a C1-smooth function on X with bounded nonempty support.