  It 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.
