An elementary proof of borsuk theorem
Metric Geometry
2010-10-12 v1
Abstract
In 1933, Borsuk conjectured that any bounded d-dimensional set of nonzero diameter can be broken into d + 1 parts of smaller diameter. This conjecture was disproved for large enough d, though it is true for low dimensional cases. The paper provides an alternative proof for d = 2 case.
Cite
@article{arxiv.1010.1990,
title = {An elementary proof of borsuk theorem},
author = {Dian Yang},
journal= {arXiv preprint arXiv:1010.1990},
year = {2010}
}
Comments
2 pages, 1 figure, this note is one of the results of my participation in `Math in Moscow' program