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
▼ Closure point
▼ Set closure
▼ Topologically dense set
Definition D99
Separable topological space
Formulation 3
A D1106: Topological space $T = (X, \mathcal{T})$ is a separable topological space if and only if there exists a D11: Set $S \subseteq X$ such that
(1) \begin{equation} \forall \, U \in \mathcal{T} \left( U \neq \emptyset \quad \implies \quad U \cap E \neq \emptyset \right) \end{equation}
(2) $S$ is a D16: Countable set