 Biholomorphism

In the mathematical theory of functions of one or more complex variables, and also in complex algebraic geometry, a biholomorphism or biholomorphic function is a bijective holomorphic function whose inverse is also holomorphic.Formally, a "biholomorphic function" is a function formula_1 defined on an open subset "U" of the formula_2-dimensional complex space C"n" with values in C"n" which is holomorphic and one-to-one, such that its image is an open set formula_3 in C"n" and the inverse formula_4 is also holomorphic.