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