Geometriae Dedicata

, Volume 29, Issue 3, pp 279–291 | Cite as

On support points of segmentally closed convex bodies in the rational plane

  • Vera Mardešić
Article
  • 18 Downloads

Abstract

In the rational plane there exist bounded segmentally closed convex bodies with no support lines. This and other examples exhibited in this paper show that in vector spaces over non-complete ordered fields support hyperplanes of convex sets behave in a way very different from the way they behave in vector spaces over the field of real numbers.

Keywords

Convex Body Convex Polygon Support Point Rational Plane Smooth Point 

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References

  1. 1.
    Brønsted, A.,An Introduction to Convex Polytopes, Springer-Verlag, Berlin, 1983.CrossRefGoogle Scholar
  2. 2.
    Eggleston, H. G.,Convexity, Cambridge Univ. Press, Cambridge, 1958.CrossRefMATHGoogle Scholar
  3. 3.
    Klee, V., ‘Extreme Points of Convex Sets without Completeness of the Scalar Field’,Mathematika 11 (1964), 59–63.MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Köthe, G.,Topologische lineare Räume, Springer-Verlag, Berlin, 1960.CrossRefMATHGoogle Scholar
  5. 5.
    Straszewicz, S., ‘Über exponierte Punkte abgeschlossener Punktmengen’,Fund. Math. 24 (1935), 139–143.MATHGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • Vera Mardešić
    • 1
  1. 1.Department of Mathematics, Faculty of Mechanical EngineeringUniversity of ZagrebZagrebYugoslavia

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