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Let $M$ and $N$ be two smooth manifolds with dimensions m and n, respectively, with $m>n$. Let $f:M\to N$ a smooth map ($C^\infty$). Show that this map can't be injective.
My try: I was wondering how could I reduce this problem to the tangent space, using the differentiability condition, to work with vector spaces, where I know how to proof this result. But I was unable to do it, so any help will be useful.