Let $T = (X, \mathcal{T})$ be a D1106: Topological space.
The set of topologically dense sets in $T$ is the D11: Set
\begin{equation}
\left\{ E \subseteq X : \forall \, U \in \mathcal{T} \left( U \neq \emptyset \quad \implies \quad U \cap E \neq \emptyset \right) \right\}
\end{equation}