# If $F:\mathbb{R}^{m} \rightarrow \mathbb{R}^{m}$ if of class $C^{1}$ …

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.

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Traducelo a ingles que no te van contestar!!! –  Marvin Gaye Oct 24 '12 at 0:01
Peruano???? Donde estudias?? Saludos de otro Peruano! que milagro encontrar un peruano en este sitio.... –  Marvin Gaye Oct 24 '12 at 0:03
Si, peruano estudio en San Marcos. –  helmonio Oct 24 '12 at 0:07
Que anho vas??? –  Marvin Gaye Oct 24 '12 at 0:08
James Munkres, usualmente. –  helmonio Oct 24 '12 at 0:13