Disjoint union (topology)
SPACE FORMED BY EQUIPPING THE DISJOINT UNION OF THE UNDERLYING SETS WITH A NATURAL TOPOLOGY CALLED THE DISJOINT UNION TOPOLOGY
Topological disjoint sum; Direct sum (topology); Direct sum topology; Disjoint union topology; Topological sum; Coproduct in the category of topological spaces; Free sum; Coproduct topology
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, in the disjoint union the given spaces are considered as part of a single new space where each looks as it would alone and they are isolated from each other.