no. 1
Every compact set in 𝐂 n is a good compact set
Annales de l'Institut Fourier, Tome 20 (1970) no. 1, pp. 493-498.

Soit K un compact d’un ouvert V dans C n . On démontre l’existence d’un voisinage U de K qui satisfait la condition suivante : si f est holomorphe sur V et s’il existe une suite des polynomes qui approchent f uniformément sur un voisinage ouvert U f de K, il existe une suite de polynômes qui approchent f uniformément sur U

Let K be an compact subset of an open set V in C n . We show the existence of an open neighborhood U of K satisfying the following condition : if f is holomorphic in V and if there exists a sequence of polynomials which approximate f uniformly in some open neighborhood U f of K, there exists a sequence of polynomial which approximate f uniformly in U.

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     author = {Bj\"ork, Jan Erik},
     title = {Every compact set in ${\bf C}^n$ is a good compact set},
     journal = {Annales de l'Institut Fourier},
     pages = {493--498},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {20},
     number = {1},
     year = {1970},
     doi = {10.5802/aif.348},
     zbl = {0188.39003},
     mrnumber = {41 #7154},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.348/}
}
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Björk, Jan Erik. Every compact set in ${\bf C}^n$ is a good compact set. Annales de l'Institut Fourier, Tome 20 (1970) no. 1, pp. 493-498. doi : 10.5802/aif.348. https://aif.centre-mersenne.org/articles/10.5802/aif.348/

[1] A. Martineau, Sur les fonctionnelles analytiques et la transformation de Fourier-Borel, J. Analyse Math. 9, 1-164 (1963). | MR | Zbl

[2] Gunnig-Rossi, Analytic functions of several complex variables, Prentice Hall (1965). | Zbl

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