\begin{definition}[Definition:Basis (Topology)/Analytic Basis/Definition 2]
Let $\struct {S, \tau}$ be a topological space.
Let $\BB \subseteq \tau$.
Then $\BB$ is an analytic basis for $\tau$ {{iff}}:
:$\forall U \in \tau: \forall x \in U: \exists V \in \BB: x \in V \subseteq U$
\end{definition}