523: Contractible Topological Space

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definition of contractible topological space

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Topics

About: topological space

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The table of contents of this article

• Starting Context
• Target Context
• Orientation
• Main Body
• 1: Structured Description
• 2: Natural Language Description

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Starting Context

• The reader knows a definition of homotopic maps.

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Target Context

• The reader will have a definition of contractible topological space.

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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.

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Main Body

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1: Structured Description

Here is the rules of Structured Description.

Entities:
$\ast T$: $\in \{\text{ the topological spaces }\}$
//

Conditions:
$\mathrm{\exists }{f}_c:T\to T,\in \{\text{ the constant maps }\}$
(
$id\simeq f_c$, where $id$ is the identity map, $id:T\to T$
).
//

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2: Natural Language Description

Any topological space, $T$, on which the identity map, $id:T\to T$, is homotopic to a constant map, $f_c:T\to T$

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References

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