Tori can't collapse to an interval

<p style='text-indent:20px;'>Here we prove that under a lower sectional curvature bound, sequence of Riemannian manifolds diffeomorphic to the standard <inline-formula><tex-math id="M1">$ m $</tex-math></inline-formula>-dimensional torus cannot converge in Gromov–Hausdorff sense closed interval.</p><p style='text-indent:20px;'>The proof is done by contradiction analyzing suitable covers contradicting sequence, obtained from Burago–Gromov–Perelman generalization Yamaguchi fibration theorem.</p>