##  [Cross-Cap](/cross-cap) 

  ##  [Cross-Cap](https://puremath.quantumdictionary.io/cross-cap-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A local model of a nonorientable surface immersion into three-space exhibiting a one-sided self-intersection called a cross-cap; it represents the local image of a neighborhood in the projective plane under an immersion that identifies opposite directions, producing a characteristic double locus.