Definition:Continuous Complex Function

Definition
As the complex plane is a metric space, the same definition of continuity applies to complex functions as to metric spaces.

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 $a \in A_1$.

Also see

 * Equivalence of Definitions of Continuous Complex Function