Abstract
In this short note, we provide the 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.
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