- #1

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R^2->R^2

(x/(x^2+y^2), y/(x^2+y^2)

is a diffeomorphism, and if it is not restrict the values so it is one

I am fairly sure it is not over R^2 as it is not continous at 0, but I don't know what values to restrict it over. I have tried to find the inverse but to no avail, thanks in advance