Separating families of convex sets
  Two elements, $x$ and $y$, are separated by a set $S$ if it contains exactly one of $x$ and $y$. We prove that any set of $n$ points in general position in the plane can be separated by $O(n\log\log n/\log n)$ convex sets, and for some point sets $\Omega(n/\log n)$ convex sets are necessary. 
D. Gerbner, G. T\'oth
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