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  "body": "\n## Summary\n\nA univalent function is a holomorphic function that is injective on its domain.\nIt is a conformal map of its domain onto its image, which is again an open set.\nThe theory of univalent functions studies the class $S$ of univalent functions on the unit disc with $f(0) = 0$ and $f'(0) = 1$.\nIts main results are distortion, covering and coefficient theorems, such as the [[Koebe quarter theorem|WX0HMW4GT7]] and the [[Bieberbach conjecture|ZMRFSYVWQT]].\n\n## Explanations\n\n### L1 human\n\nA univalent function never takes the same value twice.\nSo it maps its domain onto a region without folding or overlapping, like a sheet of rubber stretched without tearing or doubling.\nThe map $z \\mapsto z^2$ is not univalent on the unit disc, since $z$ and $-z$ have the same square.\nOn the right half-plane, $z \\mapsto z^2$ is univalent, and its image is the plane minus the negative real axis and $0$.\n",
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