2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125492We give a proof of the celebrated stability theorem of Perelman stating that for a noncollapsing sequence $X_i$ of Alexandrov spaces with curvature bounded below Gromov-Hausdorff converging to a compact Alexandrov space $X$, $X_i$ is homeomorphic to $X$ for all large $i$.revised introductionDifferential Geometry53C20text