The Topology of the set of line Transversals

Abstract

We prove that for any set $F$ of $n\ge 2$ pairwise disjoint open convex sets in ${\mathbb{R}}^3$, the connected components of the set of lines intersecting every member of $F$ are contractible. The same result holds for directed lines.

The contents of this manuscript was published as part of the paper: O. Cheong, X. Goaoc, A. F. Holmsen, Some New Results on Geometric Transversals. Discrete Comput Geom (2023)

References in corpus (1)

• Topological transversals to a family of convex sets

Cited by in corpus (1)

• An $({\aleph }_0,k+2)$-Theorem for $k$-Transversals