# Definition:Connected Set (Complex Analysis)

## Definition

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

### Definition 1

$D$ is connected if and only if every pair of points in $D$ can be joined by a staircase contour.

### Definition 2

$D$ is connected if and only if every pair of points in $D$ can be joined by a polygonal path all points of which are in $D$.

## Also see

• Results about connected sets can be found here.