##  [Nerve Construction](/nerve-construction) 

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

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The nerve construction of an open cover U = {U_i} of a topological space X is the simplicial complex N(U) whose n-simplices correspond to nonempty intersections of n+1 distinct elements of the cover; it encodes the intersection pattern of the cover as a combinatorial object.