Sections of Serre Fibrations with Low-Dimensional Fibers

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
A. "Alex" Chigogidze, Professor and Department Chair (Creator)
Institution
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/

Abstract: 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.

Additional Information

Publication
arXiv:math/0208192v1 [math.GT] 24 Aug 2002
Language: English
Date: 2002
Keywords
Serre fibration, Section, Selection, Approximation