, Volume 10, Issue 2, pp 195-202

First online:

Convexly independent sets

  • T. BisztriczkyAffiliated withDepartment of Mathematics and Statistics, University of Calgary
  • , G. Fejes TóthAffiliated withMathematical Institute of the Hungarian Academy of Sciences

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A family of pairwise disjoint compact convex sets is called convexly independent, if none of its members is contained in the convex hull of the union of the other members of the family. The main result of the paper gives an upper bound for the maximum cardinalityh(k, n) of a family ℱ of mutually disjoint compact convex sets such that any subfamily of at mostk members of ℱ is convexly independent, but no subfamily of sizen is.

AMS subject classification (1980)

52 A 10 05 A 17