Extension of smooth functions in infinite dimensions, I: unions of convex sets
Tom 146 / 2001
Studia Mathematica 146 (2001), 201-226 MSC: Primary 46T20. DOI: 10.4064/sm146-3-1
Let $f$ be a smooth function defined on a finite union $U$ of open convex sets in a locally convex Lindelöf space $E$. If, for every $x\in U$, the restriction of $f$ to a suitable neighbourhood of $x$ admits a smooth extension to the whole of $E$, then the restriction of $f$ to a union of convex sets that is strictly smaller than $U$ also admits a smooth extension to the whole of $E$.