Definitions from Wiktionary (disjoint union)

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




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