%0 Journal Article
%T Positive-fraction intersection results and variations of weak epsilon-nets
%A Alexander Magazinov
%A Pablo Sober¨Žn
%J Mathematics
%D 2015
%I arXiv
%X Given a finite set $X$ of points in $R^n$ and a family $F$ of sets generated by the pairs of points of $X$, we explore conditions for the sets that allow us to guarantee the existence of a positive-fraction subfamily $F'$ of $F$ for which the sets have non-empty intersection. This allows us to show the existence of weak epsilon-nets for these families. We also prove a topological variation of weak epsilon-nets for convex sets.
%U http://arxiv.org/abs/1506.02191v1