##  [Mapping Cylinder](/index.php/mapping-cylinder) 

  ##  [Mapping Cylinder](https://puremath.quantumdictionary.io/mapping-cylinder-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

Given a continuous map f: X→Y, the mapping cylinder Mf is the space obtained by taking X×[0,1] disjoint union Y and identifying each (x,1)∈X×{1} with f(x)∈Y; equivalently it is X×[0,1] ⊔_f Y. It provides a model for a homotopy between f and a cofibration inclusion of X into Mf.