##  [Quotient Topology](/quotient-topology) 

  ##  [Quotient Topology](https://puremath.quantumdictionary.io/quotient-topology-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The topology on a quotient set Y = X/∼ determined as the coarsest topology making the canonical projection q: X → Y continuous; a subset V ⊂ Y is declared open iff q^{-1}(V) is open in X.