Definition:Open Region

Definition

Complex Analysis

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.

Open Region in the Plane

An open region is a region without its boundary, i.e. the interior of such a region.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): open region
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): open region