On the Surjectivity of Smooth Maps into Euclidean Spaces and the Fundamental Theorem of Algebra

摘要

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 any C-1-map from a compact manifold into Euclidean space with dimension has infinitely many critical points.