Connected and Simply Connected Domains
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# Connected and Simply Connected Domains

 Definition: The domain $D$ is Connected if every pair of points $P, Q \in D$ can be joined by a piecewise smooth curve in $D$.
 Definition: The domain $D$ is Simply Connected if every simple closed curve can be continuously shrunk to a point in $D$ that never passes out of $D$.

Recall that a simple closed curve is a curve whose initial and terminal points are the same and does not intersect itself elsewhere.

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