Polynomial Runge theorem
= Polynomial Runge theorem
If $K\subset\mathbb C$ is compact with connected complement and $f$ is holomorphic near $K$, then for each $\varepsilon>0$ there is a polynomial $p$ such that $\sup_K|p-f|<\varepsilon$.
= Polynomial Runge theorem
If $K\subset\mathbb C$ is compact with connected complement and $f$ is holomorphic near $K$, then for each $\varepsilon>0$ there is a polynomial $p$ such that $\sup_K|p-f|<\varepsilon$.