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:
 * $\displaystyle\bigcup_{(U,\phi) \in A }\left\{\phi^{-1}(V) : V \text{ is open in } U \right\} \subset X$