An interval version of separation by semispaces in max-min convexity

TL;DR

This paper extends the concept of separation in max-min convexity to interval cases, providing conditions for when a box can be separated from a convex set by semispaces, and exploring related separation scenarios.

Contribution

It introduces an interval extension of separation results in max-min convexity and offers a constructive proof under specific conditions.

Findings

Separation is possible under certain conditions.

Separation is impossible if conditions are not met.

The study covers separation by boxes and semispaces.

Abstract

We study separation of a closed box from a max-min convex set by max-min semispace. This can be regarded as an interval extension of known separation results. We give a constructive proof of the separation in the case when the box and the max-min convex set satisfy certain condition, and we show that separation is never possible if this condition does not hold. We also study separation of max-min convex sets by boxes and by box and semispace.