The theorem of the representation in conformity of Riemann classifies the simply related parts of $\backslash \; mathbb\; \{C\}$.

Statement

That is to say $\backslash \; Omega$ open of $\backslash \; mathbb\; \{C\}$, distinct from $\backslash \; mathbb\; \{C\}$ and simply related. Then there exists a function $f$ holomorphic on $\backslash \; Omega$, bijective, whose reciprocal one is holomorphic, such as $f\; (\backslash \; Omega)\; =\; D\; (0,1)$, where $D\; (0,1)$ is the disc of center 0 and 1. Moreover, for $x\_0\; \backslash \; in\; \backslash \; Omega$, one can impose that $f\; (x\_0)\; =0$ and that $f\; \text{'}(x\_0)\; >0$, in which case $f$ is the single application which makes the deal.

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