Definition:Connected Domain (Complex Analysis)
Jump to navigation Jump to search
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.
- 2001: Christian Berg: Kompleks funktionsteori $\S 1.3$