##  [Initial Topology](/initial-topology) 

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

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The coarsest topology on a set X that makes a given family of maps {f_i : X → Y_i} continuous; it is generated by taking all inverse images f_i^{-1}(U) of open sets U ⊆ Y_i as a subbasis.