##  [Whitehead Theorem](/whitehead-theorem) 

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

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A criterion in homotopy theory that a map f: X → Y between CW complexes (or more generally between connected weak CW-like spaces) is a homotopy equivalence if and only if it induces isomorphisms on all homotopy groups π_n for every basepoint (equivalently, is a weak homotopy equivalence under suitable hypotheses).