## Existence of a sequence of polynomials using Rounge’s theorem

I want to use the Rounge’s theorem: if $Ksubsetmathbb{C}$ is compact and ${a_{j}}_{j=1}^{infty}subseteqmathbb{C}cup{infty}$ is such that foe every component of $mathbb{C}^{infty}smallsetminus K$ has at least one point $a_{j}$. Then, for all $f$ holomorphic in $K$, there exists $R_{n}$ rational function with poles in $a_{n}$ such that $R_{n}to f$ uniformly on $K$. For prove that there… Read More »