Let $B$ be the open unit ball in $\mathbb{R}^n$. I need to find continuous bijective function $f: B \to \mathbb{R}^n$ such that $f^{-1}$ is also continuous.
I thought of $f(x)=\frac{1}{d(x,x_0)}$ for some $x_0 \in B$. Is it Ok regrading the conditions? I'm not really sure.. Do you have any idea for another suitable function?
Thanks a lot!