definition of deformation 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 retraction.
- The reader knows a definition of homotopic maps.
Target Context
- The reader will have a definition of deformation 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
\( \iota\): \(: T \to T', p \mapsto p\)
\( id\): \(: T' \to T', p \mapsto p\)
\(*f\): \(: T' \to T\), \(\in \{\text{ the retractions }\}\)
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Conditions:
\(\iota \circ f \simeq id\), where \(\simeq\) denotes being homotopic
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2: Natural Language Description
For any topological space, \(T'\), and any subspace, \(T \subseteq T'\), any retraction, \(f: T' \to T\), such that \(\iota \circ f \simeq id\), where \(\iota: T \to T', p \mapsto p\), \(id: T' \to T', p \mapsto p\), and \(\simeq\) denotes being homotopic
