Abstract It is proven by elementary methods that in dimension 2, every locally injective continuous map, sending the curves of a Ck-spray to curves of another Ck-spray as oriented point sets, is a Ck-diffeomorphism. This extends the result [1] for dimension three and higher from 1965.

中文翻译：

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维 2 中投影变换的可微性

摘要 用初等方法证明，在第2维上，每一个局部单射连续映射，将一个Ck-spray的曲线发送到另一个Ck-spray的曲线作为有向点集，是一个Ck-微分同胚。这扩展了 1965 年第三维及更高维度的结果 [1]。