Sigma-Algebra Generated by Complements of Generators

Theorem
Let $\Sigma$ be a $\sigma$-algebra on a set $X$.

Let $\GG$ be a generator for $\Sigma$.

Then:


 * $\GG' := \set {X \setminus G: G \in \GG}$

the set of relative complements of $\GG$, is also a generator for $\Sigma$.

Proof
Hence the result.