Stoïlow’s theorem from 1928 states that a continuous, open, and light map between surfaces is a discrete map with a discrete branch set. This result implies that such maps between orientable surfaces are locally modeled by power maps $z\mapsto z^k$ and admit a holomorphic factorization.

The purpose of this expository article is to give a proof of this classical theorem having readers in mind that are interested in continuous, open and discrete maps.

中文翻译：

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斯托伊洛定理再探

1928年的斯托伊洛定理指出，曲面之间的连续，开放和光照贴图是具有离散分支集的离散贴图。该结果表明，可定向曲面之间的此类贴图由功率贴图局部建模。$ž\mapsto {ž}^{ķ}$ 并接受全纯分解。

这篇说明性文章的目的是在考虑到对连续，开放和离散地图感兴趣的读者的情况下，提供这一经典定理的证明。