  We show that the Radon number characterizes the existence of weak nets in
separable convexity spaces (an abstraction of the euclidean notion of
convexity). The construction of weak nets when the Radon number is finite is
based on Helly's property and on metric properties of VC classes. The lower
bound on the size of weak nets when the Radon number is large relies on the
chromatic number of the Kneser graph. As an application, we prove a
boosting-type result for weak $\epsilon$-nets.
