Define fundamental group
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The fundamental group of an arcwise-connected set is the group formed by the sets of equivalence classes of the set of all loops, i.e., paths with initial and final points at a given basepoint , under the equivalence relation of homotopy.
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In the mathematical field of algebraic topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of the loops contained in the space. It records information about the basic shape, or holes, of the topological space.
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