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 $C^1$-map from a compact manifold into Euclidean space with dimension $n\ge2$ has infinitely many critical points.
On radii of spheres determined by subsets of Euclidean space
A simple proof of the Fundamental Theorem of Calculus for the Lebesgue integral
The Fundamental Theorem of Algebra: From The Four Basic Operations
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