DanielMcGinnis

We solve a long-standing open problem posed by Goodman and Pollack in 1988 by establishing a necessary and sufficient condition for a finite family of convex sets in ${\mathbb{R}}^d$ to admit a $k$-transversal (a $k$-dimensional affine subspace that intersects each set) for any $0\le k\le d-1$. This result is a common generalization of …