definition of wedge sum of pointed topological spaces
Topics
About: topological space
The table of contents of this article
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.
Target Context
- The reader will have a definition of wedge sum of pointed topological spaces.
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:
\( \{(T_\alpha, p_\alpha) \vert \alpha \in A\}\): \(\subseteq \{\text{ the pointed topological spaces }\}\), \(A \in \{\text{ the possibly uncountable index sets }\}\)
\( \coprod_{\alpha \in A} T_\alpha\): \(= \text{ the topological sum }\)
\(*\vee_{\alpha \in A} (T_\alpha, p_\alpha)\): \(= \text{ the wedge sum of the sets}\) 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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