definition of retraction
Topics
About: topological space
The table of contents of this article
- Starting Context
- Target Context
- Orientation
- Main Body
- 1: Structured Description
- 2: Natural Language Description
Starting Context
- The reader knows a definition of topological subspace.
- The reader knows a definition of continuous map.
Target Context
- The reader will have a definition of retraction.
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: Structured Description
Here is the rules of Structured Description.
Entities:
\( T'\): \(\in \{\text{ the topological spaces }\}\)
\( T\): \(\subseteq T'\), with the subspace topology
\(*f\): \(: T' \to T\), \(\in \{\text{ the continuous maps }\}\)
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Conditions:
\(\forall p \in T (f (p) = p)\)
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2: Natural Language Description
For any topological space, \(T'\), and any subspace, \(T \subseteq T'\), any continuous map, \(f: T' \to T\), such that \(\forall p \in T (f (p) = p)\)
