Mathematical Programming

, Volume 18, Issue 1, pp 84–88 | Cite as

Borsuk's theorem through complementary pivoting

  • Imre Bárány
Short Communication


In this short note a simple and constructive proof is given for Borsuk's theorem on antipodal points. This is done through a special application of the complementary pivoting algorithm.

Key words

Complementary Pivot Algorithms Triangulations Vector Labels Borsuk's Theorem on Antipodal Points 


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    K. Borsuk, “Drei Sätze über dien-dimensionalische euklidische Sphäre”,Fundamenta Mathematicae 20 (1933) 177–190.Google Scholar
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    F.E. Browder, “On continuity of fixed points under deformations of continuous mappings”,Summa Brasiliensis Mathematicae 4 (1960) 183–191.Google Scholar
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    B.C. Eaves, “A short course in solving equations with PL homotopies”SIAM-AMS Proceedings 9 (1976) 73–143.Google Scholar
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Copyright information

© The Mathematical Programming Society 1980

Authors and Affiliations

  • Imre Bárány
    • 1
  1. 1.OTSZK, KTTBudapestHungary

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