We report on some recent progress regarding combinatorial properties in convexity spaces with a bounded Radon number. In particular, we discuss the relationship between the Radon number, the colorful and fractional Helly properties, weak ε-nets, and $(p,q)$-theorems. As an application of the theory of convexity spaces we introduce new classes of uniform hypergraphs and show that they are χ-bounded.
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Andreas F. Holmsen (2024) studied this question.
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