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On surjectivity of smooth maps into Euclidean spaces and the fundamental theorem of algebra (1706.07281v1)
Published 16 Jun 2017 in math.CA
Abstract: In this note we obtain the surjectivity of smooth maps into Euclidean spaces under mild conditions. As application we give a new proof of the Fundamental Theorem of Algebra. We also observe that any $C1$-map from a compact manifold into Euclidean space with dimension $n\ge2$ has infinitely many critical points.
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