##  [Spanier–Whitehead Duality](/spanier-whitehead-duality) 

  ##  [Spanier–Whitehead Duality](https://puremath.quantumdictionary.io/spanier-whitehead-duality-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A duality in stable homotopy theory that assigns to a finite (or compact) CW complex a dual object in the stable homotopy category so that maps from the smash product with the dual into the sphere spectrum identify with maps out of the original complex; informally, finite complexes have stable duals represented by suitably suspended complements.