2 problems

Let $R(K)$ denote the uniform algebra of rational functions with poles off a compact set $K\subset\mathbb{C}$. For $x\in K$, write $M_x$ for the maximal ideal of functions in…

Let $L\subset K\subset\mathbb{C}$ be compact sets, let $s\in\mathbb{Z}_+$, and let $x\in L$. For a compact set $E$ and $z\in E$, write $R(E)$ for the uniform algebra of rational fu…