I'm studying differentiation and came across this question: If $F:\mathbb{R}^{m} \rightarrow \mathbb{R}^{m}$ is of class $C^{1}$ such that $\Vert f^{\prime}(x)v\Vert \geqslant 2\Vert v\Vert$. Then F is a diffeomorphism of $\mathbb{R}^{m}$ in $\mathbb{R}^{m}$. I can not take the condition of $F$ to show that $F$ is injective. If you could help me, thanks.
If $F:\mathbb{R}^{m} \rightarrow \mathbb{R}^{m}$ if of class $C^{1}$ ...
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real-analysis
analysis
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1James Munkres, usualmente. – 2012-10-24