Convex Sets

  • Marcel Berger
  • Pierre Pansu
  • Jean-Pic Berry
  • Xavier Saint-Raymond
Part of the Problem Books in Mathematics book series (PBM)

Abstract

A subset S of X is called convex if the segment [x,y] (cf. 3.C) is contained in S for every x, yS. A weaker condition is that defining star-shaped sets: S is star-shaped with center aX if [a, x] c S for every x ∈ S. In R convex sets are the same as intervals.

Keywords

Convex Hull Affine Space Convex Compact Subset Affine Subspace Euclidean Vector Space 
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

© Marcel Berger 1984

Authors and Affiliations

  • Marcel Berger
    • 1
  • Pierre Pansu
    • 2
  • Jean-Pic Berry
    • 3
  • Xavier Saint-Raymond
    • 3
  1. 1.U.E.R. de Mathematique et InformatiqueUniversité Paris VIIParis, Cedex 05France
  2. 2.Centre National de la Recherche ScientifiqueParisFrance
  3. 3.P.U.K.GrenobleFrance

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