Simply ConnectedA Connected Domain is said to be simply connected (also called 1-connected) if any simpleclosed curve can be shrunk to a point continuously in the set. If the domain is Connected but notsimply, it is said to be Multiply Connected.
A Space is simply connected if it is 0-connected and if every Map from the 1-Sphere to extendscontinuously to a Map from the 2-Disk. In other words, every loop in the Space is contractible. See also Connected Space, Multiply Connected
|