disjoint union

disjoint union

English

Noun

disjoint union (plural disjoint unions)

1. (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).
2. (mathematics) A union of sets which are already pairwise disjoint.
3. (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

• disjoint union topology

Translations

union of sets forced to be disjoint

Italian: unione disgiunta f Swedish: disjunkt union (sv)

union of already disjoint sets

Italian: unione disgiunta f Swedish: disjunkt union (sv)

union of topologies

Icelandic: sundurlæga sammengi n

See also

• coproduct
• disjunctive union
• product topology

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)