# Definition:Open Region

## Definition

### Complex Analysis

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

$D$ is an open region 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.