Let $n\in\mathbb{N}$, and let $X$ be a nonempty compact connected [complex manifold](/page/Complex%20Manifold) of complex dimension $n$. If $f:X\to\mathbb{C}$ is holomorphic, then there exists a complex number $c\in\mathbb{C}$ such that $f(p)=c$ for every $p\in X$.