##  [Nonseparated Scheme](/nonseparated-scheme) 

  ##  [Nonseparated Scheme](https://algebra.quantumdictionary.io/nonseparated-scheme-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A scheme that fails the separation axiom: the diagonal morphism Δ: X → X×_S X is not a closed immersion (or equivalently not proper/closed), so points or morphisms that would be uniquely determined in a separated setting may fail uniqueness. Nonseparated schemes exhibit gluing pathologies such as multiple origins or failure of uniqueness of limits.