Definition:Basis (Topology)/Analytic Basis

Definition
Let $T = \left({A, \vartheta}\right)$ be a topological space.

Let $\mathcal B \subseteq \vartheta$ such that for all $U \in \vartheta$, $U$ is a union of sets from $\mathcal B$.

Then $\mathcal B$ is an analytic basis for $\vartheta$.

Also known as
Some sources do not distinguish between an analytic basis and a synthetic basis, and instead use this definition and call it a basis.

Also see

 * Synthetic Basis and Analytic Basis are Compatible