A Simpler Proof of the Boros-Füredi-Bárány-Pach-Gromov Theorem

@article{Karasev2012ASP,
  title={A Simpler Proof of the Boros-F{\"u}redi-B{\'a}r{\'a}ny-Pach-Gromov Theorem},
  author={Roman N. Karasev},
  journal={Discrete & Computational Geometry},
  year={2012},
  volume={47},
  pages={492-495}
}
A short and almost elementary proof of the Boros–Füredi–Bárány–Pach– Gromov theorem on the multiplicity of covering by simplices in R d is given. Let us give a proof of the Boros–Füredi–Bárány–Pach–Gromov theorem [1, 4, 8, 6] that is actually the " decoded " and refined proof from [6] (see also [5, Section 2] for a similar proof in the two-dimensional case). Unlike the proof in [6], the only topological notion that is used here is the degree of a piece-wise smooth map. Consider a set of d + 1… CONTINUE READING
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