The endomorphisms of the lattice of convex bodies

  • P. M. Gruber


This article contains a complete description of the endomorphisms of the lattice of compact convex subsets ofE d where the common intersection and the convex hull of the common union define the lattice operations.


Convex Body Relative Interior Lattice Operation Compact Convex Subset Collinear Point 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    G. Birkhoff, Lattice Theory, 3rd ed., Amer. Math. Soc., Providence Rh. I. 1967.MATHGoogle Scholar
  2. [2]
    R. Fourneau, Isomorphismes de lattis de fermés convexes, Bull. Soc. Math. France103 (1975), 3–12.MATHMathSciNetGoogle Scholar
  3. [3]
    R. Fourneau, Automorphism Groups of Lattices of Closed Convex Sets, J. Math. Anal. Appl.72 (1979), 21–28.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    R. Frank, Ein lokaler Fundamentalsatz für Projektionen, Manuscript 1990.Google Scholar
  5. [5]
    P.M. Gruber, The Space of Convex Bodies, in: Handbook of Convex Geometry, North-Holland, Amsterdam, In preparation.Google Scholar
  6. [6]
    K. Leichtweiss, Konvexe Mengen, Springer, Berlin 1980.Google Scholar
  7. [7]
    H. Lenz, Einige Anwendungen der projektiven Geometrie auf Fragen der Flächentheorie, Math. Nachr.18 (1958), 346–359.MATHMathSciNetGoogle Scholar

Copyright information

© Mathematische Seminar 1991

Authors and Affiliations

  • P. M. Gruber
    • 1
  1. 1.Abteilung für AnalysisTechnische Universität WienViennaAustria

Personalised recommendations