Topological properties of the zeros of a holomorphic function

Desvl at 
What’s going onIf for every $z_0 \in \Omega$ where $\Omega$ is a plane open set, the limit\[ \lim_{z \to z_0}\frac{f(z)-f(z_0)}{z-z_0}\]exists, we say that $f$ is holomorphic (a.k.a. analytic) in $\Omega$. If $f$ is holomorphic in the whole plane, it’s called entire. The class of all holomorphic ……