Definition:Topology Generated by Synthetic Basis

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

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

It is shown in Union from Synthetic Basis is a Topology that $\vartheta$ is a topology on $X$.

Also see

 * Generated Topology