Leírás
Steinitz's theorem states that if a point is in the interior of the convex hull of a set X in R^d, then X contains a subset Y of size at most 2d such that the same point lies in the interior of the convex hull of Y. Easy examples show that the bound 2d is best possible here. The colourful version of this theorem has been known for quite some time. Our main result is the characterization of the case when exactly 2d sets are needed. Joint work with Yun Qi.