Definition:Connected Domain (Complex Analysis)

Definition
Let $D \subseteq \C$ be a subset of the set of complex numbers.

Then $D$ is a connected domain $D$ is open and connected.

Also defined as
A connected domain $D$ is often used as the domain of a complex-differentiable function $f: D \to \C$.

Also known as
Some texts omit the word connected and simply call $D$ a domain.

Also see

 * Open Domain is Connected iff it is Path-Connected


 * Requirement for Connected Domain to be Simply Connected Domain