Theorem
180
[244]\(β\) is the smallest S-saturated set.
Proof
Given a set \(A\) that is S-saturated, \(β_ A\) is defined as the intersection of all S-saturated subsets of \(A\). By [245], \(β_ A\) is S-saturated. Given two sets \(A,B\) that are S-saturated, it is proven that \(β_ A=β_ B\): we denote then by \(β\) this set. In particular, given a set \(A\) that is S-saturated, we have \(β\subseteq A\).