Lecture 16: Classification of singularities and Casorati–Weierstrass theorem

We prove Reimann's theorem on removable singularities and from this we can classify singularities into three types according to the blow up behavior of the function near the singularity, the three types are removable singularities, poles and essential singularities. We then prove Casorati–Weierstrass theorem that closure of the imagine of any punctured ball around an essential singularity covers the entire complex plane.