Abstract

Generalizing the concept of Choquet simplex, we study a new class of convex solids KK in Rn\mathbb{R}^n which satisfy the following condition: all nn-dimensional intersections of the form K∩(x+K)K \cap (x + K), x∈Rnx \in \mathbb{R}^n, belong to at most finitely many homothety classes of convex solids. Our description of this class uses new results on boundedly polyhedral sets.

Author information

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

Valeriu Soltan

Dept. of Mathematical Sciences, George Mason University, Fairfax, U.S.A.

vsoltan@gmu.edu

Keywords

  • Convex set
  • Choquet simplex
  • homothety class
  • polyhedron

Mathematics Subject Classification

52A20

References

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Suggested citation

V. Soltan. “Boundedly Polyhedral Sets and F-Simplices.” Journal of Convex Analysis 29 (2022), No. 3, 807–826. https://doi.org/10.68381/jca29047

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Published by Heldermann Verlag, 2022. Rights now held by Banach Press.