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

Let $T_{\mathbb{C}} = (\mathbb{C}, \mathcal{T}_{\mathbb{C}})$ be the D5778: Standard complex topological space such that

(i)	$T_{\Omega} = (\Omega, \mathcal{T}_{\Omega})$ is a D100: Topological subspace of $T_{\mathbb{C}}$

Then $T_{\Omega}$ is a complex domain if and only if

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