Corpus ID: 18501664

A cubical antipodal theorem

  title={A cubical antipodal theorem},
  author={K. Kinneberg and Aaron Mazel-Gee and Tia Sondjaja and F. Su},
  • K. Kinneberg, Aaron Mazel-Gee, +1 author F. Su
  • Published 2009
  • Mathematics
  • The classical Lusternik-Schnirelman-Borsuk theorem states that if a d-sphere is covered by d+1 closed sets, then at least one of the sets must contain a pair of antipodal points. In this paper, we prove a combinatorial version of this theorem for hypercubes. It is not hard to show that for any cover of the facets of a d-cube by d sets of facets, at least one such set contains a pair of antipodal ridges. However, we show that for any cover of the ridges of a d-cube by d sets of ridges, at least… CONTINUE READING

    Figures from this paper.


    Publications referenced by this paper.
    Ein Beweis des Fixpunktsatzes für n-dimensionale Simplexe
    • 478
    • Highly Influential
    • PDF
    Drei Sätze über die n-dimensionale euklidische Sphäre
    • 462
    • Highly Influential
    • PDF
    Ein Beweis des Fixpunktsatzes für ndimensionale Simplexe , Fund
    • 1933
    Some Topological Properties of the Disk and Sphere
    • 1945
    Topological Methods in Variational Calculus, IssledowatelskiIssledowatelskiˇIssledowatelskiˇi Institut Matematiki i Mechaniki pri