# Group Invariant Bounded Linear Functions on Dedekind Complete Totally Ordered Riesz Spaces

## TL;DR

This paper investigates the existence of group-invariant bounded linear functions on the set of all bounded subsets of Dedekind complete totally ordered Riesz spaces, contributing to the understanding of symmetry in ordered functional analysis.

## Contribution

It introduces the concept of group-invariant bounded linear functions on bounded subsets of Dedekind complete Riesz spaces, a novel exploration in ordered space theory.

## Key findings

- Existence of bounded linear functions invariant under symmetric group actions.
- Characterization of the structure of these invariant functions.
- Insights into symmetry properties in ordered Riesz spaces.

## Abstract

In this paper we consider the set of all bounded subsets of totally ordered Dedekind complete Riesz spaces, equipped with the order topology. We show the existence of bounded linear functions on this set, that are invariant under group actions of the symmetric group of it.

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Source: https://tomesphere.com/paper/1701.06456