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
Canonical name	TopologicalSum
Date of creation	2013-03-22 14:41:29
Last modified on	2013-03-22 14:41:29
Owner	rspuzio (6075)
Last modified by	rspuzio (6075)
Numerical id	7
Author	rspuzio (6075)
Entry type	Definition
Classification	msc 54A99
Synonym	coproduct in the category of topological spaces
Synonym	topological disjoint union