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
▼ Set of topologically dense sets
Definition D4812
Topological space density
Formulation 0
Let $T = (X, \mathcal{T})$ be a D1106: Topological space such that
(i) $\mathcal{D} = \mathcal{D}(T)$ is the D3111: Set of topologically dense sets in $T$
The density of $T$ is the D15: Set cardinality \begin{equation} \inf_{D \in \mathcal{D}} |D| \end{equation}