3 papers
math.GT2009
Local section of Serre fibrations with 3-manifold fibers
N. Brodsky, A. Chigogidze, E. V. Shchepin
It was proved by H. Whitney in 1933 that a Serre fibration of compact metric spaces admits a global section provided every fiber is homeomorphic to the unit interval [0,1]. An exte…
math.GT2002
Sections of Serre fibrations with low-dimensional fibers
N. Brodsky, A. Chigogidze, E. V. Shchepin
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…
math.AT2002
Hurewicz theorem for extension dimension
N. Brodsky, A. Chigogidze
We prove a new selection theorem for multivalued mappings of C-space. Using this theorem we prove extension dimensional version of Hurewicz theorem for a closed mapping $f\colon X\…