Analytic germ projection
= Analytic germ projection
{title2=$\pi([f]_z)=z$}
The projection $[f]_z\mapsto z$ is a local <biholomorphism> for the sheet topology on the <space of germs of holomorphic functions>. It need not be a topological <covering map>: branches may end at singularities even when another branch remains over that base point.