##  [Smash Product](/smash-product) 

  ##  [Smash Product](https://puremath.quantumdictionary.io/smash-product-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

For pointed spaces (X,x0) and (Y,y0), the smash product X ∧ Y is the quotient of the product X × Y obtained by collapsing the wedge X ∨ Y (i.e., X × {y0} ∪ {x0} × Y) to a single basepoint; it is a pointed analogue of the reduced tensor for spaces.