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Hometopological sum

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# topological sum

*topological sum* is defined
to be the set $X\coprod Y$ (see the entry *disjoint union*) equipped with
the finest topology such that the inclusion maps from $X$ and $Y$ into $X\coprod Y$
are continuous. A basis for this topology consists of the union of the set of
open subsets of $X$ and the set of open subsets of $Y$.

Synonym:

coproduct in the category of topological spaces, topological disjoint union

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

54A99*no label found*

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