Branch point

Summary

A branch point of a multivalued function is a point with this property: going once around it along a small loop changes the value. See the definition. The square root has branch points at $0$ and $\infty$, and so does the complex logarithm. Branch points are the reason for branch cuts. When the function is made single-valued on a Riemann surface, they become the ramification points of a branched covering.