##  [C\_0 Space](/c0-space) 

  ##  [C\_0 Space](https://puremath.quantumdictionary.io/c0-space-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The space C_0(X) of continuous scalar-valued functions on a locally compact Hausdorff space X that vanish at infinity, meaning for every ε>0 there exists a compact K ⊂ X with |f(x)| < ε for x outside K; typically equipped with the supremum norm when X is noncompact.