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A Connected Domain is said to be simply connected (also called 1-connected) if any simple closed curve can be shrunk to a point continuously in the set. If the domain is Connected but not simply, 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 extends
continuously to a Map from the 2-Disk. In other words, every loop in the Space is contractible.
See also Connected Space, Multiply Connected