can anyone give me an example and explain why any open set in $\mathbb{C}$ is a domain of holomorphy?
I have understood the fact from here but not able to understand their explanation for $n=1$
can anyone give me an example and explain why any open set in $\mathbb{C}$ is a domain of holomorphy?
I have understood the fact from here but not able to understand their explanation for $n=1$
It's clear that $\mathbb{C}$ itself is a domain of holomorphy.
For other domains, let $p$ be a boundary point of $\Omega$ and put $f(z) = \frac{1}{z-p}.$ Then $f$ is holomorphic on $\Omega$ (indeed on $\mathbb{C} \setminus \{ p \}$) and can't be extended across $p$.