Corollary 3

Let $g\in G$, and let C be its centralizer. Then $g$ belongs to $C_0$; the group $C_0$ is the union of the maximal tori of G containing $g$.

There exists a maximal torus T of G containing $g$ (Th. $2c$)$)$, and hence contained in $C_0$. Moreover, the group $C_0$ is a connected compact Lie group, and hence the union of its maximal tori (Th. $2c$)$)$; these all contain $g$ (Cor. 2), hence are exactly the maximal tori of G containing $g$.