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Jun 13, 2015 at 17:19 vote accept Cepu
Jun 12, 2015 at 8:28 comment added Cepu Since $\mathbb{R}^{n}$ is a convenient vector space as well, I can apply the results of this paper to my problem. But i don't understand why in the proposition 1.9 they show that the extension exists if the convex set is closed, with non-empty interior, and with smooth boundary. Assume that $C$ is a triangle in $\mathbb{R}^{2}$, and consider $f\: : \: C\to \mathbb{R}$, does the extension exists ?
Jun 11, 2015 at 18:28 history edited Peter Michor CC BY-SA 3.0
added 94 characters in body
Jun 11, 2015 at 15:52 history answered Peter Michor CC BY-SA 3.0