On the separation theorems for convex sets on the unit sphere

TL;DR

This paper presents a new proof for a recent theorem on separating convex sets on the unit sphere, utilizing concepts from locally convex spaces to simplify the argument.

Contribution

It offers an alternative proof for the separation theorem on spherical convex sets, connecting it to locally convex space theory.

Findings

New proof of the separation theorem for spherical convex sets

Connection established between spherical convexity and locally convex spaces

Simplification of existing proof techniques

Abstract

In this short note we provide a new proof of the recent result of Han and Nashimura on the separation of spherical convex sets established in arXiv:2002.06558. Our proof is based on a result stated in locally convex spaces.