Connected and Simply Connected Domains

# 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.*