Definition:Continuous Complex Function/Using Limit

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 $a \in A_1$.

$f$ is continuous at (the point) $a$ if and only if:

The limit of $\map f z$ as $z \to a$ exists, and

$\ds \lim_{z \mathop \to a} \map f z = \map f a$

Also see

• Equivalence of Definitions of Continuous Complex Function

• Results about continuous complex functions can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): continuous function (continuous mapping)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): continuous function (continuous mapping, continuous map)