2 problems

Let $(X,\mathcal C)$ be an abstract convexity space with Radon number $D$, and let $\operatorname{Tv}_{\mathcal C}(r)$ denote its Tverberg number for $r$ parts. Eckhoff's partition…

Carathéodory-number conjecture. For a function from $L$ to be an optimal approximation in uniform norm, it is enough that it is optimal at $c(\mathcal{C}_{H_L})+1$ extreme points.…