Corollary

The set of $g\in G$ such that $T\cap gTg^{-1}\not= C(G)$ is the union of a finite number of closed analytic submanifolds of G distinct from G.

Indeed, put $A_g= T\cap gTg^{-1}$; we have $T\subset Z(A_g)$ and $gTg^{-1}\subset Z(A_g)$. Hence, there exists $x\in Z(A_g)$ such that $xTx^{-1}=gTg^{-1}($§2, no. 2, Th. 2), which implies that $g\in Z(A_g).N_G(T)$. Denote by $\mathscr{A}$ the finite (Cor. 1) set of closed subgroups of G containing T and distinct from G, and put X = $\bigcup_{H\in\mathscr{A}}H.N_G(T)$; this is a finite union of closed submanifolds of G, distinct from G. If $A_g\not= C(G)$, then $Z(A_g)\in \mathscr{A}$, and $g$ belongs to X. Conversely, if $g\in H.N_G$(T), with $H\in \mathscr{A}$, then $A_g$ contains C(H), so $A_g\not= C(G)$ (Prop. 13).