##  [Homotopy Equivalence](/homotopy-equivalence) 

  ##  [Homotopy Equivalence](https://puremath.quantumdictionary.io/homotopy-equivalence-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A continuous map f: X → Y is a homotopy equivalence if there exists a continuous g: Y → X such that g ∘ f is homotopic to id_X and f ∘ g is homotopic to id_Y; X and Y are then said to have the same homotopy type.