We give necessary and sufficient condition for an infinite collection of
axis-parallel boxes in Rd to be pierceable by finitely many
axis-parallel k-flats, where 0≤k<d. We also consider colorful
generalizations of the above result and establish their feasibility. The
problem considered in this paper is an infinite variant of the
Hadwiger-Debrunner (p,q)-problem.Comment: 13 page