Definition:Continuous Complex Function/Open Sets

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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 if and only if:

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


Also see

  • Results about continuous complex functions can be found here.


Sources