A definition of quotient map
Topics
About: topological space
The table of contents of this article
Starting Context
- The reader knows a definition of continuous map.
- The reader knows a definition of surjection.
Target Context
- The reader will have a definition of quotient map.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Definition
For any topological spaces, \(T_1, T_2\), any continuous surjection, \(f: T_1 \rightarrow T_2\), such that for any subset, \(S \subseteq T_2\), if \(f^{-1} (S)\) is open, \(S\) is open
