Zermelo’s postulate

If $ℱ$ is a disjoint family of nonempty sets, then there is a set $C$ which has exactly one element of each $A\in ℱ$ (i.e such that $A\cap C$ is a singleton for each $A\in ℱ$.)

This is one of the many propositions that are equivalent to the axiom of choice.

Title	Zermelo’s postulate
Canonical name	ZermelosPostulate
Date of creation	2013-03-22 13:13:36
Last modified on	2013-03-22 13:13:36
Owner	Koro (127)
Last modified by	Koro (127)
Numerical id	6
Author	Koro (127)
Entry type	Theorem
Classification	msc 03E25
Related topic	AxiomOfChoice
Related topic	MaximalityPrinciple
Related topic	TukeysLemma
Related topic	ZornsLemma
Related topic	KuratowskisLemma