Über konvexe Körper

  title={{\"U}ber konvexe K{\"o}rper},
  author={D. K{\"o}nig},
  journal={Mathematische Zeitschrift},
  • D. König
  • Published 1 December 1922
  • Mathematics
  • Mathematische Zeitschrift
A note on the colorful fractional Helly theorem
  • Minki Kim
  • Computer Science, Mathematics
    Discret. Math.
  • 2017
An improved version of Barany et al.'s result, obtaining a colorful fractional Helly theorem, concerning the intersection patterns of convex sets in R d.
Carathéodory’s Theorem in Depth
A depth version of Carathéodory’s theorem is proved and it is proved that there exist a constant c (that depends only on d and $$\tau _X(q)$$τX (q)) and pairwise disjoint sets X such that the following holds.
Convexity without convex combinations
Separation theorems play a central role in the theory of Functional Inequalities. The importance of Convex Geometry has led to the study of convexity structures induced by Beckenbach families. The
First Things First on Convex Sets
A. Convex Sets. We begin here with some basic definitions and elementary facts. Throughout this book we will work in an n-dimensional real vector space \(\mathcal{X}\). The choice of a basis in
Helly, Radon, and Carathéodory Type Theorems
This chapter discusses applications and generalizations of the classical theorems of Helly, Radon, and Caratheodory, as well as their ramifications in the context of combinatorial convexity theory.
Characterization of weakly efficient points
Weakly efficient points of a mappingF: S → Y are characterized, where the feasible setS is given by infinitely many constraints, andY is equipped with an arbitrary convex ordering. In the linear and
Eulers Charakteristik und kombinatorische Geometrie.
Die klassische Elementargeometrie bezieht sieh bekanntlich vorwiegend auf lineare und polyedrische Gebilde des euklidischen Raumes. Erweitert man den Rahmen, indem man die Betrachtungen auch auf die