398: Topological Sum

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A definition of topological sum

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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.

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Target Context

• The reader will have a definition of topological sum

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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 family of topological spaces, $\{T_{\alpha }\}$ where $\{\alpha \}$ is any possibly uncountable indexes set, the disjoint union, $\coprod _{\alpha }{T}_{\alpha }$, with the topology such that any subset, $S\subseteq \coprod _{\alpha }{T}_{\alpha }$ is open if and only if $S\cap T_{\alpha }$ is open for each $\alpha$, often denoted like $T_1+T_2$ when the indexes set is finite

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References

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