disjoint union

Short definition from Wiktionary

Noun

1. 1
   A union of sets forced to be disjoint by attaching information referring to the original sets to their elements (i.e., by using indexing).
2. 2
   A union of sets which are already pairwise disjoint.
3. 3
   The disjoint union of the underlying sets of a given family of topological spaces, equipped with a topology.