399: Adjunction Topological Space Obtained by Attaching Topological Space via Map to Topological Space

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A definition of adjunction topological space obtained by attaching topological space via map to 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: Definition

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Starting Context

• The reader knows a definition of topological space.
• The reader knows a definition of continuous map.
• The reader knows a definition of topological sum.

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Target Context

• The reader will have a definition of adjunction topological space obtained by attaching topological space via map to 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: Definition

For any topological spaces, $T_1,T_2$, any subset, $S\subseteq T_1$, and any continuous map, $f:S\to T_2$, the quotient space of the topological sum, $T_1+T_2$, such that any point, $p\in f(S)$, and all the points of the set, $f^{-1}(p)\subseteq S$, are identified, is the adjunction topological space obtained by attaching $T_1$ via $f$ to $T_2$, denoted as $T_2{\cup }_f{T}_1$

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References

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