##  [Classifying Space](/classifying-space) 

  ##  [Classifying Space](https://puremath.quantumdictionary.io/classifying-space-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A topological space BG associated to a topological group G such that (principal) G‑bundles over a space X correspond bijectively (up to isomorphism) to homotopy classes of maps X → BG; often realized via a contractible total space EG with free G‑action and BG = EG/G.