About an Erd\H{o}s-Gr\"unbaum conjecture concerning piercing of non   bounded convex sets
  In this paper, we study the number of compact sets needed in an infinite family of convex sets with a local intersection structure to imply a bound on its piercing number, answering a conjecture of Erd\H{o}s and Gr\"unbaum. Namely, if in an infinite family of convex sets in $\mathbb{R}^d$ we know that out of every $p$ there are $q$ which are intersecting, we determine if having some compact sets implies a bound on the number of points needed to intersect the whole family. We also study variations of this problem. 
Amanda Montejano, Luis Montejano, Edgardo Rold\'an-Pensado, Pablo   Sober\'on
math.MG