Domains of Analyticity in Real Normed Spaces

We essentially prove that there is a C∞ function ƒ on the separable real normed space E which is analytic on E\M, analytic at no point of M and such that its restriction to E\M has no analytic extension at any point of the border of M in the following two cases: • satisfies the Kurzweil condition and is a closed subset of , • is a weakly closed subset of . In particular, if the real normed space E is separable • and satisfies the Kurzweil condition, every domain of is a domain of analyticity, • every weak domain of is a domain of analyticity.