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The fundamental group of a Connected Set is the Quotient Group of the Group of all paths with initial
and final points at a given point
and the Subgroup of all paths Homotopic to the
degenerate path consisting of the point
.
The fundamental group of the Circle is the Infinite Cyclic Group. Two fundamental groups having different
points are Isomorphic. If the fundamental group consists only of the identity element, then
the set
is Simply Connected.
See also Milnor's Theorem