THEOREM OF THE DAY: Neumann’s Separation Lemma

Theorem

Let G be a permutation group acting on an infinite set Ω with no finite orbits. Then for any finite subsets Γ and ∆ of Ω there exists a permutation g ∈ G for which $Γ^g ∩ ∆ = ∅$.

 

Click on the image.