A pathwise-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.
In particular, a bounded subset 
of 
is said to be simply connected if both 
and 
, where 
denotes a set difference,
are connected.
A space 
is simply connected if it is pathwise-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.
