617: Retract of Topological Space

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definition of retract of 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 retraction.

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Target Context

• The reader will have a definition of retract of 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:
$T^{\prime }$: $\in \{\text{ the topological spaces }\}$
$\ast T$: $\subseteq T^{\prime }$, with the subspace topology
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Conditions:
$\mathrm{\exists }f:T^{\prime }\to T(f\in \{\text{ the retractions }\})$
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2: Natural Language Description

For any topological space, $T^{\prime }$, any subspace, $T\subseteq T^{\prime }$, such that there is a retraction, $f:T^{\prime }\to T$

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References

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