topological sum

Given two topological spaces $X$ and $Y$, their topological sum is definedto be the set $X\coprod Y$ (see the entry disjoint union) equipped withthe 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 ofopen subsets of $X$ and the set of open subsets of $Y$.