##  [Hurewicz Theorem](/hurewicz-theorem) 

  ##  [Hurewicz Theorem](https://puremath.quantumdictionary.io/hurewicz-theorem-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A theorem that compares homotopy and homology by stating that for a path-connected space X the Hurewicz homomorphism from the first nontrivial homotopy group to homology is an isomorphism under connectivity hypotheses; more generally it identifies the first nonzero homotopy group with the corresponding homology group when lower homotopy vanishes.