Let $\mathbb{C}$ be the D5778: Standard complex topological space such that

(i)	$\Omega \subseteq \mathbb{C}$ is a D100: Topological subspace of $\mathbb{C}$

Then $\Omega$ is a complex domain if and only if

(1)	$\Omega$ is an D97: Open set in $\mathbb{C}$
(2)	$\Omega$ is a D1116: Connected topological space