Definition:Basis (Topology)/Analytic Basis/Definition 2

Definition
Let $\left({S, \tau}\right)$ be a topological space.

Let $\mathcal B \subseteq \tau$.

Then $\mathcal B$ is an analytic basis for $\tau$ :
 * $\forall U \in \tau: \forall x \in U: \exists B \in \mathcal B: x \in B \subseteq U$

Also see

 * Equivalence of Definitions of Analytic Basis