In
general topology and related areas of
mathematics, the
disjoint union (also called the
direct sum,
free union,
free sum,
topological sum, or
coproduct) of a family of
topological spaces is a space formed by equipping the
disjoint union of the underlying sets with a
natural topology called the
disjoint union topology. Roughly speaking, two or more spaces may be considered together, each looking as it would alone.