I am looking for a $C^\infty $ map $f: \textbf R^2 \longrightarrow \textbf R^2 $ where $Df(0,0)$ is singular but $f^{-1}$ exist globally and is continuous.
Can someone help me?
2026-04-13 13:59:47.1776088787
Looking for example (infinitely many times differentiable)
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You can take $f(x,y)=(x,y^3)$, for instance. Its inverse is $f^{-1}(x,y)=\left(x,\sqrt[3]y\right)$, which is continuous.