Skip to main content
SpringerLink
Log in

The ham sandwich theorem revisited

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. Alon,Some recent combinatorial applications of Borsuk-type theorems, inAlgebraic, Extremal and Metric Combinatorics, Cambridge Univ. Press, Cambridge, 1988, pp. 1–12

    Google Scholar 

  2. P. Billingsley,Convergence of Probability Measures, John Wiley & Sons, 1968.

  3. S. Bogatii,Topological methods in combinatorial problems (in russian), Uspehi Mathematicheskih Nauk41 (1986), 37–48.

    Google Scholar 

  4. L. Danzer, B. Grünbaum, and V. Klee,Helly’s theorem and its relatives, inConvexity, Proc. Symp. Pure Math. VIII, AMS, 1963.

  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.

    Article  MathSciNet  Google Scholar 

  6. B. Knaster,Problem 4, Colloq. Math.1 (1947), 30.

    Google Scholar 

  7. V. V. Makeev,On some properties of continuous mappings of spheres and problems of combinatorial geometry (in russian), to appear.

  8. J. W. Milnor and J. D. Stasheff,Characteristic Classes, Princeton Univ. Press, 1974.

  9. R. Rado,A theorem on general measure, J. London Math. Soc.21 (1946), 291–300.

    Article  MathSciNet  Google Scholar 

  10. R. Živaljević and S. Vrećica,An extension of the ham sandwich theorem, Bull. London Math. Soc.22 (1990), 183–186.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mathematics, Studentski trg 16, 11001, Beograd, p.p. 550, Yugoslavia

    Sinisa T. Vrećica

  2. Mathematics Institute, Knez Mihailova 35/1, 11001, Beograd, p.p. 367, Yugoslavia

    Rade T. Živaljević

Authors
  1. Sinisa T. Vrećica
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rade T. Živaljević
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vrećica, S.T., Živaljević, R.T. The ham sandwich theorem revisited. Israel J. Math. 78, 21–32 (1992). https://doi.org/10.1007/BF02801568

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02801568

Keywords

Search

Navigation