Definition:Basis (Topology)/Analytic Basis/Definition 1

Definition
Let $\struct {S, \tau}$ be a topological space.

An analytic basis for $\tau$ is a subset $\BB \subseteq \tau$ such that:
 * $\displaystyle \forall U \in \tau: \exists \AA \subseteq \BB: U = \bigcup \AA$

That is, such that for all $U \in \tau$, $U$ is a union of sets from $\BB$.

Also see

 * Equivalence of Definitions of Analytic Basis