# topological sum

Given two topological spaces $X$ and $Y$, their 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 $Y$.

Title topological sum TopologicalSum 2013-03-22 14:41:29 2013-03-22 14:41:29 rspuzio (6075) rspuzio (6075) 7 rspuzio (6075) Definition msc 54A99 coproduct in the category of topological spaces topological disjoint union