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

## Definition

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

An analytic basis for $\tau$ is a subset $\mathcal B \subseteq \tau$ such that:

$\displaystyle \forall U \in \tau: \exists \mathcal A \subseteq \mathcal B: U = \bigcup \mathcal A$

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

## Also see

• Results about analytic bases can be found here.