On the surjectivity of smooth maps into Euclidean spaces and the
On the surjectivity of smooth maps into Euclidean spaces and the
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关于欧几里得空间的光滑映射的满射性和
DOI：
10.1080/00029890.2018.1521241
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Liu Shibo
中科院分区：
文献类型：
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作者：
Liu Peng;Liu Shibo
本文在较弱的条件下得到了欧氏空间中光滑映射的满射性。作为应用，给出了代数基本定理的一个新证明。我们还观察到从紧致流形到维数为的欧氏空间的任何C1-映射都有无穷多个临界点。
In this note, we obtain the surjectivity of smooth maps into Euclidean spaces under mild conditions. As an application, we give a new proof of the fundamental theorem of algebra. We also observe that anyC1-map from a compact manifold into Euclidean space with dimensionhas infinitely many critical points.