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Example: The most important example is the topological space <math>S^1</math>. It can be shown that the fundamental group of <math>S^1</math> is isomorphic to the additive group of [[integer]]s <math>\mathbf{Z}</math>.
Example: The most important example is the topological space <math>S^1</math>. It can be shown that the fundamental group of <math>S^1</math> is isomorphic to the additive group of [[integer]]s <math>\mathbf{Z}</math>.
In addition to aiding in the classification of topological spaces, methods in algebraic topology considerably simplify some proofs in [[abstract algebra]]. For example, the proof that there is an injection from the free group on three generators to the free group on two generators is most easily expressed in terms of the topological concept of covering spaces.
[[Category:Topology]]
[[Category:Topology]]
[[Category:Algebra]]
[[Category:Algebra]]