Tverberg-type theorems for intersecting by rays

TL;DR

This paper explores intersection properties between rays and convex sets, extending classical theorems like the center point theorem and Tverberg's theorem to new geometric configurations.

Contribution

It introduces Tverberg-type theorems specifically for intersecting rays with convex sets, expanding the scope of classical intersection theorems.

Findings

Established new Tverberg-type intersection results for rays and convex sets

Extended classical theorems to ray-based geometric configurations

Provided conditions under which intersections occur

Abstract

In this paper we consider some results on intersection between rays and a given family of convex, compact sets. These results are similar to the center point theorem, and Tverberg's theorem on partitions of a point set.