Let $(M^{n}_{j},g_{j},p_{j})$ be a sequence of Riemannian manifolds satisfying $|{\rm Ric}_{M^{n}_{j}}|\to 0$, ${\rm Vol}(B_{1}(p_{j}))>{\rm v}>0$ and such that

$\displaystyle(M_{j}^{n},d_{j},p_{j})\to\mathds{R}^{n-3}\times C(Y)\,,$

(5.10)

in the pointed Gromov-Hausdorff sense, where $Y$ is some compact metric space. Then $Y=S^{2}(1)$ is isometric to the unit $2$-sphere and hence $\mathds{R}^{n-3}\times C(Y)=\mathds{R}^{n}$.