Definition:Topology Induced by Atlas

Definition
Let $X$ be a set.

Let $A$ be an atlas on $X$.

The topology induced by the atlas is the topology generated by the synthetic sub-basis:
 * $\ds \bigcup_{\tuple {U, \phi} \mathop \in A} \set {\map {\phi^{-1} } V : V \text { is open in } U} \subset X$