##  [Covering Space](/covering-space) 

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

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A topological space C together with a continuous surjective map p: C → X (the covering map) onto a base space X such that every point of X has an open neighborhood U for which p^{-1}(U) is a disjoint union of open sets in C, each of which is mapped homeomorphically onto U by p. The fibers p^{-1}(x) are discrete sets and p is a local homeomorphism.