ThmDex – An index of mathematical definitions, results, and conjectures.
 ▼ Set of symbols ▼ Alphabet ▼ Deduction system ▼ Theory ▼ Zermelo-Fraenkel set theory ▼ Set ▼ Subset ▼ Power set ▼ Hyperpower set sequence ▼ Hyperpower set ▼ Hypersubset ▼ Subset algebra ▼ Subset structure ▼ Topological space ▼ Open set ▼ Standard open real function set ▼ Standard open euclidean real set ▼ Standard open complex set
Definition D4898
Complex domain

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