On idempotent convexities and idempotent barycenter maps

TL;DR

This paper explores the relationship between two types of idempotent convexities and their barycenter maps, revealing topological properties through an isomorphism involving maximum, addition, and multiplication operations.

Contribution

It establishes an isomorphism between max-addition and max-multiplication based idempotent convexities, enabling analysis of barycenter map properties.

Findings

Identifies an isomorphism between two idempotent convexities.

Analyzes topological properties of barycenter maps.

Provides insights into the structure of idempotent measure convexity.

Abstract

We consider an isomorphism between the idempotent convexity based on the maximum and the addition operations and the idempotent measure convexity on the maximum and the multiplication operations. We use this isomorphism to investigate topological properties of the barycenter map related to the maximum and the multiplication operations.