Biholomorphism/Definition

Property of a holomorphic function $f$ from $A\subseteq \mathbb {C}$ to $B\subseteq \mathbb {C}$ characterized in that there exist holomorphic function $g=f^{-1}$ : $f{\big (}g(z){\big )}\!=\!z~\forall z\in B~$ and $g{\big (}f(z){\big )}\!=\!z~\forall z\in A~$.