Definition:Open Region/Complex

Definition

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

$D$ is an open region of $\C$ if and only if $D$ is:

$(1): \quad$ An open set

and

$(2): \quad$ connected.

Also known as

An open region is also known as a (complex) domain.

Also see

• Results about open regions of the complex plane can be found here.

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Point Sets: $8.$