Given a smooth manifold $M$, call an open set $A \subseteq M$ a chart domain iff there exists a chart $(U,\Phi)$ in the maximal atlas on $M$ such that $A=U.$
Question. If I've got two chart domains $A,B \subseteq M$, what conditions do I need on the intersection $A \cap B$ before I can conclude that $A \cup B$ is itself a chart domain?