# Definition:Topology Generated by Synthetic Basis

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## Definition

Let $S$ be a set.

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

### Definition 1

The **topology on $S$ generated by $\mathcal B$** is defined as:

- $\displaystyle \tau = \left\{{\bigcup \mathcal A: \mathcal A \subseteq \mathcal B}\right\}$

### Definition 2

## Also see

- Union from Synthetic Basis is Topology, which proves that $\tau$ is a topology on $S$