A definition of adjunction topological space obtained by attaching topological space via map to topological space
Topics
About: topological space
The table of contents of this article
Starting Context
- The reader knows a definition of topological space.
- The reader knows a definition of continuous map.
- The reader knows a definition of topological sum.
Target Context
- The reader will have a definition of adjunction topological space obtained by attaching topological space via map to topological space.
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 subset, \(S \subseteq T_1\), and any continuous map, \(f: S \rightarrow T_2\), the quotient space of the topological sum, \(T_1 + T_2\), such that any point, \(p \in f (S)\), and all the points of the set, \(f^{-1} (p) \subseteq S\), are identified, is the adjunction topological space obtained by attaching \(T_1\) via \(f\) to \(T_2\), denoted as \(T_2 \cup_f T_1\)
