Solution
= Solution
Take $\Omega=\{|z|<1\}$, $K=\{|z|=1\}$, and $\zeta=0$. These satisfy the stated connectedness and disjointness conditions. If <polynomials> $P_n$ converged uniformly to $1/z$ on $K$, convergence of the contour integrals would imply
$$
0=\lim_n\int_{|z|=1}P_n(z)\,dz=\int_{|z|=1}\frac{dz}{z}=2\pi i,
$$
a contradiction to the <Cauchy integral theorem>. Thus \b[boundedness of this $\Omega$ permits the obstruction] excluded in part (b).