##  [Nerve Lemma](/nerve-lemma) 

  ##  [Nerve Lemma](https://puremath.quantumdictionary.io/nerve-lemma-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A statement relating the homotopy type of a topological space covered by a collection of sets to the simplicial nerve of that cover: if a cover of a space is 'good' (each finite nonempty intersection of sets in the cover is contractible), then the nerve simplicial complex is homotopy equivalent to the union (the original space).