geometry, complex numbers, complex line
$dim = 1$: Riemann surface, super Riemann surface
A biholomorphic function is a holomorphic function which is a bijection on the underlying sets and whose set-theoretic inverse is also holomorphic.
If $f:U\to V$ is a bijective holomorphic map of open subsets of complexfied Cartesian space ${\mathbb{C}}^n$, then the determinant of the Jacobian $J(f)$ is nowhere $0$, that is $f^{-1}$ is holomorphic.
(See this MO discussion and also this other MO discussion)
Last revised on July 19, 2014 at 20:49:23. See the history of this page for a list of all contributions to it.