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d-Convexity in normed spaces

  • Vladimir Boltyanski
  • Horst Martini
  • Petru S. Soltan
Chapter
Part of the Universitext book series (UTX)

Abstract

In this chapter we consider basic properties of d-convex sets in finite-dimensional normed spaces. Central subjects are the support properties of d-convex sets (§10) and the properties of d-convex flats (§11). This chapter is of decisive importance for developing a machinery for solving combinatorial problems. Nevertheless, it is interesting for itself, because the family of d-convex sets has far-reaching analogies to the family of convex sets in R n . For example, the carrying flats, faces, inscribed cones, and supporting cones of d-convex sets are d-convex themselves; moreover, each boundary point of a d-convex body is contained in a d-convex supporting hyperplane. Questions referring to separability of d-convex sets are considered in section 13 of this chapter.

Keywords

Unit Ball Normed Space Convex Body Minkowski Space Nonempty Intersection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Vladimir Boltyanski
    • 1
  • Horst Martini
    • 2
  • Petru S. Soltan
    • 3
  1. 1.Steklov Mathematical InstituteMoscowRussia
  2. 2.Faculty of MathematicsTU Chemnitz-ZwickauChemnitzGermany
  3. 3.Faculty of MathematicsMoldavian State UniversityKishinevMoldova

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