Theorems of Caratheodory, Helly, and Tverberg without dimension

摘要

Motivated by Barman, we initiate a systematic study of the 'no-dimensional' analogues of some basic theorems in combinatorial and convex geometry, including the colorful Caratheodory's theorem, Tverberg's theorem, Helly's theorem as well as their fractional and colorful extensions.