%0 Journal Article
%T Sections of Serre fibrations with low-dimensional fibers
%A N. Brodsky
%A A. Chigogidze
%A E. V. Shchepin
%J Mathematics
%D 2002
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0208192v1