# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## 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

#### Streszczenie

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 $E$.

#### Autorzy

• C. J. AtkinSchool of Mathematical and Computing Sciences
Victoria University of Wellington
P.O. Box 600
Wellington, New Zealand
e-mail

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