\begin{definition}[Definition:Basis (Topology)/Analytic Basis/Definition 1]
Let $\struct {S, \tau}$ be a topological space.
An '''analytic basis for $\tau$''' is a subset $\BB \subseteq \tau$ such that:
:$\ds \forall U \in \tau: \exists \AA \subseteq \BB: U = \bigcup \AA$
That is, such that for all $U \in \tau$, $U$ is a union of sets from $\BB$.
\end{definition}