definition of contractible topological space
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 homotopic maps.
Target Context
- The reader will have a definition of contractible 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: Structured Description
Here is the rules of Structured Description.
Entities:
\(*T\): \(\in \{\text{ the topological spaces }\}\)
//
Conditions:
\(\exists f_c: T \to T, \in \{\text{ the constant maps }\}\)
(
\(id \simeq f_c\), where \(id\) is the identity map, \(id: T \to T\)
).
//
2: Natural Language Description
Any topological space, \(T\), on which the identity map, \(id: T \to T\), is homotopic to a constant map, \(f_c: T \to T\)
