# Definition:Connected Domain (Complex Analysis)

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## Definition

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

Then $D$ is a **connected domain** if and only if $D$ is open and connected.

### Simply Connected Domain

Let $D \subseteq \C$ be a connected domain.

Then $D$ is called a **simply connected domain** if and only if $D$ is simply 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

## Sources

- 2001: Christian Berg:
*Kompleks funktionsteori*$\S 1.3$