High Quality Content by WIKIPEDIA articles! 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 ? defined on an open subset U of the n-dimensional complex space Cn with values in Cn which is holomorphic and one-to-one, such that its image is an open set V in Cn and the inverse phi^{-1}:Vto U is also holomorphic. More generally, U and V can be complex manifolds. One can prove that it is enough for ? to be holomorphic and one-to-one in order for it to be biholomorphic onto its image.

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