Return to Revisions

Consider the following map $f$ from $\mathbb R^2$ to the torus $\mathbb T^2=\mathbb R^2/\mathbb Z^2$: $$ f(x,y) = (x, \sqrt2 y) \bmod \mathbb Z^2 . $$ Its set of critical values equals its image and it is dense in the torus, so the $\epsilon$-neighborhood has full measure for any $\epsilon>0$.