Sections of Serre fibrations with low-dimensional fibers

Brodsky, N.; Chigogidze, A.; Shchepin, E. V.

Sections of Serre fibrations with low-dimensional fibers

Authors

Brodsky, N.

Chigogidze, A.

Shchepin, E. V.

Description

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.
22 pages