Riemann domain over C^n

Summary

A Riemann domain over $\C^n$ is a connected space that lies over $\C^n$ through a local homeomorphism, possibly with several sheets over the same point. It is the several-variable analogue of a Riemann surface spread over the plane. Riemann domains are needed because analytic continuation of a holomorphic function can lead to several values over one point. The envelope of holomorphy of a domain in $\C^n$ is in general a Riemann domain and not a subset of $\C^n$.