Commentary on Menger’s Work on Curve Theory and Topology

  • Tony Crilly
  • Alan Moran


Part of the attractiveness of the theory of curves to the young Karl Menger was its place in the mainstream of mathematics. The concept of a curve has changed over the centuries depending upon contemporary mathematical theories, and, in this historical process, Menger has played a significant part.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    G. A. Dirac, Généralisations du théorème de Menger. C. R. Acad. Sci. Paris 250 (1960) 4252–4253.MathSciNetzbMATHGoogle Scholar
  2. [2]
    G. A. Dirac, Short proof of Menger’s graph theorem. Mathematika 13 (1966) 42–44.MathSciNetCrossRefGoogle Scholar
  3. [3]
    B. Knaster, Atti Congr. Int. Mat. Bologna 2 (1928) 225.Google Scholar
  4. [4]
    D. König, Theorie der endlichen und unendlichen Graphen. Acad. Verl. Ges., Leipzig 1936.zbMATHGoogle Scholar
  5. [5]
    K. Kuratowski, Sur le problème des courbes gauches en topologie. Fund. Math. 15 (1930) 271–283.CrossRefGoogle Scholar
  6. [6]
    K. Menger, Zur allgemeinen Kurventheorie. Fund. Math. 10 (1927) 96–115.CrossRefGoogle Scholar
  7. [7]
    K. Menger, Uber plättbare Dreiergraphen und die Potenzen nicht-plättbarer Graphen. Akad. Wiss. Wien 67 (1930) 30–31.zbMATHGoogle Scholar
  8. [8]
    K. Menger, Kurventheorie. B. G. Teubner, Leipzig (1932); reprinted, Chelsea Publ., New York (1967).zbMATHGoogle Scholar
  9. [9]
    C. St. J. A. Nash-Williams and W. T. Tutte, More proofs of Menger’s Theorem. J. Graph Theory 1 (1977) 13–14.MathSciNetCrossRefGoogle Scholar
  10. [10]
    G. Nöbeling, Eine Verschärfung des n-Beinsatzes. Fund. Math. 18 (1932) 23–38.CrossRefGoogle Scholar
  11. [11]
    W. Sierpiński, Sur une courbe dont tout point est un point de ramification. C. R. Acad. Sci. Paris 173 (1915) 302–305.zbMATHGoogle Scholar
  12. [12]
    P. Urysohn, Mémoire sur les multiplicités Cantoriennes II. Verhand. Akad. Amsterdam. 1. Sect. No. 4 13 (1927) 1–172.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Wien 2002

Authors and Affiliations

  • Tony Crilly
  • Alan Moran

There are no affiliations available

Personalised recommendations