About an Erdős–Grünbaum Conjecture Concerning Piercing of Non-bounded Convex Sets

  title={About an Erdős–Gr{\"u}nbaum Conjecture Concerning Piercing of Non-bounded Convex Sets},
  author={Amanda Montejano and Luis Pedro Montejano and Edgardo Rold{\'a}n-Pensado and Pablo Sober{\'o}n},
  journal={Discrete \& Computational Geometry},
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 Erdős and Grünbaum. Namely, if in an infinite family of convex sets in $$\mathbb {R}^d$$Rd we know that out of every $$p$$p there are $$q$$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… 


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