# 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 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.