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

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.

References in corpus (3)

• The number of extreme points of tropical polyhedra
• Cyclic projectors and separation theorems in idempotent convex geometry
• On hyperplanes and semispaces in max-min convex geometry

Cited by in corpus (1)

• On the dimension of max-min convex sets