Suppose $x,y \in \mathbb{R}^n $. Find a diffeomorphism $F:\mathbb{R}^n \rightarrow \mathbb{R}^n$ and $r>0$ such that $F(x)=y$ and $F(z)=z$ for any $z\in \mathbb{R}^n-B(x,r)$ .
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This need that $r\geq \vert x-y\vert$. Can you do it in diemension 1 ? – Thomas Apr 14 '17 at 06:54
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I can prove the case for dim=1,but not for dim>1 – Edward Grammer Apr 14 '17 at 07:18