Abstract

In a recent paper P. Diamond, P. Kloeden, A. Rubinov and A. Vladimirov [Set-Valued Analysis (2000)] investigated comperative properties of three different metrics in the space of pairs of compact convex sets. These metrics describe invariant properties of the Radström-Hörmander lattice i.e. the space of equivalence classes of pairs of nonempty compact convex sets. In this paper we consider invariants of a class of equivalent pairs of nonempty compact convex sets. We show that the affine dimension of the minimal representant of an equivalence class is invariant and that each equivalence class has invariant convexificators.

Author information

Contact details are reproduced from the original publication and may be historical.

Diethard Pallaschke

Inst. f. Statistik und Mathematische Wirtschaftstheorie, Universität Karlsruhe, Kaiserstr. 12, 76128 Karlsruhe, Germany

Ryszard Urbański

Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland

Keywords

  • Pairs of convex sets
  • sublinear function
  • quasidifferential calculus

Mathematics Subject Classification

52A07; 26A27, 90C30

References

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Suggested citation

D. Pallaschke, R. Urbański. “Invariants of Pairs of Compact Convex Sets.” Journal of Convex Analysis 6 (1999), No. 2, 367–376. https://doi.org/10.68381/jca06021

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Published by Heldermann Verlag, 1999. Rights now held by Banach Press LLC.