2023-01-29

398: Topological Sum

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A definition of topological sum

Topics


About: topological space

The table of contents of this article


Starting Context



Target Context


  • The reader will have a definition of topological sum

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: 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


References


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