(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

f:R^{n}->R^{n}is continuous and satisfies

|f(x)-f(y)|>=k|x-y|

for all x, y in R^{n}and some k>0. Show that F has a continuous inverse.

2. Relevant equations

3. The attempt at a solution

It is easy to show that f is injective, but I've no idea how to prove the surjectivity. I was thinking on the R^{1}->R^{1}case for a while, and guess that I can show that f is unbounded to deduce the surjectivity. But it seems that boundedness is not that useful in R^{n}->R^{n}case.

Any hint? THanks!

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# Homework Help: Continuity, vector function, inverse

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