English

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.

Keywords

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

R2 v1 2026-06-21T16:26:28.797Z