Definition:Continuous Complex Function/Open Sets

Definition
Let $A_1, A_2 \subseteq \C$ be subsets of the complex plane.

Let $f: A_1 \to A_2$ be a complex function from $A_1$ to $A_2$.

Let $A_1$ be open in $\C$.

$f$ is continuous :
 * for every set $U \subseteq \C$ which is open in $\C$, $f^{-1} \sqbrk{ U }$ is open in $\C$.