Israel Journal of Mathematics

, Volume 78, Issue 1, pp 21–32 | Cite as

The ham sandwich theorem revisited

  • Sinisa T. Vrećica
  • Rade T. Živaljević


This paper continues the search, started in [10], for relatives of the ham sandwich theorem. We prove among other results, the following implications {fx21-1} whereK(n, k) is an important instance of the Knaster’s conjecture so thatK(n, n − 1) reduces to the Borsuk-Ulam theorem,B(n, k) is a R. Rado type statement about (k + 1) measures inR n whereB(n, n − 1) turns out to be the ham sandwich theorem andC(n, k) is a topological statement, established in this paper in the caseC(n, n − 2),n = 3 orn ≥ 5.


Vector Bundle Spectral Sequence Euler Class Grassmann Manifold Canonical Bundle 
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  1. [1]
    N. Alon,Some recent combinatorial applications of Borsuk-type theorems, inAlgebraic, Extremal and Metric Combinatorics, Cambridge Univ. Press, Cambridge, 1988, pp. 1–12Google Scholar
  2. [2]
    P. Billingsley,Convergence of Probability Measures, John Wiley & Sons, 1968.Google Scholar
  3. [3]
    S. Bogatii,Topological methods in combinatorial problems (in russian), Uspehi Mathematicheskih Nauk41 (1986), 37–48.Google Scholar
  4. [4]
    L. Danzer, B. Grünbaum, and V. Klee,Helly’s theorem and its relatives, inConvexity, Proc. Symp. Pure Math. VIII, AMS, 1963.Google Scholar
  5. [5]
    E. Fadell and S. Husseini,An ideal-valued cohomological index theory with applications to Borsuk-Ulam and Bourgain-Yang theorems, Ergodic Theory & Dynamical Systems8 (1988), 73–85.MathSciNetCrossRefGoogle Scholar
  6. [6]
    B. Knaster,Problem 4, Colloq. Math.1 (1947), 30.Google Scholar
  7. [7]
    V. V. Makeev,On some properties of continuous mappings of spheres and problems of combinatorial geometry (in russian), to appear.Google Scholar
  8. [8]
    J. W. Milnor and J. D. Stasheff,Characteristic Classes, Princeton Univ. Press, 1974.Google Scholar
  9. [9]
    R. Rado,A theorem on general measure, J. London Math. Soc.21 (1946), 291–300.CrossRefMathSciNetGoogle Scholar
  10. [10]
    R. Živaljević and S. Vrećica,An extension of the ham sandwich theorem, Bull. London Math. Soc.22 (1990), 183–186.CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© The Magnes Press 1992

Authors and Affiliations

  • Sinisa T. Vrećica
    • 1
  • Rade T. Živaljević
    • 2
  1. 1.Faculty of MathematicsBeograd, p.p. 550Yugoslavia
  2. 2.Mathematics InstituteBeograd, p.p. 367Yugoslavia

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