disjoint union
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English
Noun
disjoint union (plural disjoint unions)
- (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).
- (mathematics) A union of sets which are already pairwise disjoint.
- (topology) The disjoint union of the underlying sets of a given family of topological spaces, equipped with a topology.
Usage notes
The two senses defining unions of sets are rarely distinguished with much care, except in a very formal setting. In category theory, they are essentially identical: both are realisations of the coproduct of a category of sets.
Synonyms
- (union of sets forced to be disjoint): discriminated union
- (union of already disjoint sets): discriminated union
- (union of topological spaces equipped with a topology): coproduct, direct sum, free sum, free union, topological sum
Derived terms
Translations
union of sets forced to be disjoint
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union of already disjoint sets
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union of topologies
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See also
Further reading
Disjoint union (topology) on Wikipedia.Wikipedia - Disjoint union of graphs on Wikipedia.Wikipedia
- Disjoint union on Encyclopedia of Mathematics
- disjoint union on nLab
- Disjoint Union on Wolfram MathWorld (which uses a formal structure equivalent to an index)
