857: Wedge Sum of Pointed Topological Spaces

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definition of wedge sum of pointed topological spaces

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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

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Starting Context

• The reader knows a definition of wedge sum of pointed sets.
• The reader knows a definition of topological sum.
• The reader knows a definition of quotient topology on set with respect to map.

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Target Context

• The reader will have a definition of wedge sum of pointed topological spaces.

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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:
$\{(T_{\alpha },p_{\alpha })|\alpha \in A\}$: $\subseteq \{\text{ the pointed topological spaces }\}$, $A\in \{\text{ the possibly uncountable index sets }\}$
$\coprod _{\alpha \in A}{T}_{\alpha }$: $=\text{ the topological sum }$
$\ast {\vee }_{\alpha \in A}(T_{\alpha },p_{\alpha })$: $=\text{ the wedge sum of the sets}$ with the quotient topology with respect to $f$
$f$: $:\coprod _{\alpha \in A}{T}_{\alpha }\to {\vee }_{\alpha \in A}(T_{\alpha },p_{\alpha })$, $=\text{ the canonical map that maps }{p}_{\alpha }\text{ to }[p_{\alpha }]$
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Conditions:
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References

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