##  [Quotient Map](/quotient-map) 

  ##  [Quotient Map](https://mathlogic.quantumdictionary.io/quotient-map-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A surjective continuous map q : X -> Y that endows Y with the quotient topology: a subset U of Y is open iff q^{-1}(U) is open in X. Equivalently, q is final for continuous maps from X, identifying points according to an equivalence relation and making Y the coarsest space for which q is continuous.