Definition:Connected Set (Complex Analysis)
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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.