# relation as union of functions

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

This proposition of Doran is equivalent (http://planetmath.org/Equivalent3) to the Axiom of Choice (http://planetmath.org/AxiomOfChoice).

## References

• 1 R. S. Doran: “A Theorem which is Equivalent to the Axiom of Choice”.  – Elemente der Mathematik 27 (1972).
Title relation as union of functions RelationAsUnionOfFunctions 2013-03-22 15:24:08 2013-03-22 15:24:08 Mathprof (13753) Mathprof (13753) 7 Mathprof (13753) Theorem msc 03E25 AxiomOfChoice