I have this problem, Let $\omega$ a closed $1$ form in $\mathbb{R^{2}}\setminus {0} $ such that $\omega$ restricted to the set $D$ is bounded with $D=\left \{ x\in\mathbb{R} \text{ such that }\left | x \right |<r\right \}$ Is it right that $\omega$ is exact? Proof or counter example.
Help, thanks!