Every compact set in ${𝐂}^n$ is a good compact set

Björk, Jan Erik. "Every compact set in ${\bf C}^n$ is a good compact set." Annales de l'institut Fourier 20.1 (1970): 493-498. <http://eudml.org/doc/74010>.

@article{Björk1970,
abstract = {Let $K$ be an compact subset of an open set $V$ in $\{\bf C\}^n$. 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 $U$.},
author = {Björk, Jan Erik},
journal = {Annales de l'institut Fourier},
keywords = {complex functions},
language = {eng},
number = {1},
pages = {493-498},
publisher = {Association des Annales de l'Institut Fourier},
title = {Every compact set in $\{\bf C\}^n$ is a good compact set},
url = {http://eudml.org/doc/74010},
volume = {20},
year = {1970},
}

TY - JOUR
AU - Björk, Jan Erik
TI - Every compact set in ${\bf C}^n$ is a good compact set
JO - Annales de l'institut Fourier
PY - 1970
PB - Association des Annales de l'Institut Fourier
VL - 20
IS - 1
SP - 493
EP - 498
AB - Let $K$ be an compact subset of an open set $V$ in ${\bf C}^n$. 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 $U$.
LA - eng
KW - complex functions
UR - http://eudml.org/doc/74010
ER -