Oka–Weil theorem
In mathematics, especially the theory of several complex variables, the Oka–Weil theorem is a result about the uniform convergence of holomorphic functions on Stein spaces due to Kiyoshi Oka and André Weil. == Statement == The Oka–Weil theorem states that if X is a Stein space and K is a compact O ( X ) {\displaystyle {\mathcal {O}}(X)} -convex subset of X, then every holomorphic function in an open neighborhood of K can be approximated uniformly on K by holomorphic functions on O ( X ) {\displaystyle {\mathcal {O}}(X)} (in particular, by polynomials).