1. The problem statement, all variables and given/known data f:Rn->Rn is continuous and satisfies |f(x)-f(y)|>=k|x-y| for all x, y in Rn 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 R1->R1 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 Rn->Rn case. Any hint? THanks!