2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64773It was proved by H. Whitney in 1933 that it is possible to mark a point in all curves in a continuous way. The main result of this paper extends the Whitney theorem to dimensions 2 and 3. Namely, we prove that it is possible to choose a point continuously in all two-dimensional surfaces sufficiently close to a given surface, and in all 3-manifolds sufficiently close to a given 3-manifold.22 pagesGeometric Topology57N05text