Definition:Topology Generated by Synthetic Basis/Definition 1

Definition
Let $S$ be a set.

Let $\mathcal B$ be a synthetic basis of $S$.

The topology on $S$ generated by the $\mathcal B$ is defined as:
 * $\displaystyle \tau = \left\{{\bigcup \mathcal A: \mathcal A \subseteq \mathcal B}\right\}$