Definition:Topology Generated by Synthetic Basis

Definition
Let $\mathcal B$ be a synthetic basis on a set $S$.

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

Also see

 * Union from Synthetic Basis is Topology


 * Generated Topology