On a question of supports

TL;DR

This paper establishes a sufficient condition for n closed connected subsets in n-dimensional real projective space to share a common multitangent hyperplane.

Contribution

It provides a new criterion ensuring the existence of a common multitangent hyperplane for multiple subsets in projective space.

Findings

Identifies a sufficient condition for common multitangent hyperplanes.

Applicable to n closed connected subsets in n-dimensional space.

Advances understanding of geometric configurations in projective space.

Abstract

We give a sufficient condition in order that $n$ closed connected subsets in the $n$-dimensional real projective space admit a common multitangent hyperplane.