PlanetMath: relation as union of functions

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relation as union of functions

(Theorem)

Every relation $R$ is a union of functions with the same domain as $R$

Bibliography

1: R. S. DORAN: ``A Theorem which is Equivalent to the Axiom of Choice''. - Elemente der Mathematik 27 (1972).

"relation as union of functions" is owned by Mathprof. [ owner history (1) ]

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See Also: axiom of choice

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Attachments:: proof that a relation is union of functions if and only if AC (Proof) by ratboy

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Cross-references: proposition, domain, functions, union, relation
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This is version 4 of relation as union of functions, born on 2005-07-19, modified 2006-02-17.
Object id is 7241, canonical name is RelationAsUnionOfFunctions.
Accessed 1999 times total.

Classification:

03E25 (Mathematical logic and foundations :: Set theory :: Axiom of choice and related propositions)

Pending Errata and Addenda

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