We assume in this question that $U$ is path-connected. Determine the set of functions $f$ in $\mathcal{H}(U)$ such that $f^2$ also belongs to $\mathcal{H}(U)$.
We assume in this question that $U$ is path-connected. Determine the set of functions $f$ in $\mathcal{H}(U)$ such that $f^2$ also belongs to $\mathcal{H}(U)$.