Definition:Topology Generated by Synthetic Basis/Definition 3

Definition
Let $S$ be a set.

Let $\BB$ be a synthetic basis of $S$.

The topology on $S$ generated by $\BB$ is defined as:
 * $\tau = \set {U \subseteq S: \forall x \in U: \exists B \in \BB: x \in B \subseteq U}$