3 problems

Let $\mathcal F$ be the family of bottomless rectangles in the plane, and let $m_k^*(\mathcal F)$ denote the corresponding threshold for decomposing coverings into $k$ coverings. B…

Projected-family piercing conjecture. There exists a constant $A$ such that every finite family of axis-parallel rectangles satisfies

Wegner's conjecture. Every finite family of axis-parallel rectangles in $\mathbb{R}^2$ satisfies