Handelman's theorem for an order unit normed space

TL;DR

This paper provides a detailed proof of Handelman's theorem, establishing that a monotone sigma-complete order unit normed space is necessarily a Banach space, thus linking order-theoretic and topological properties.

Contribution

The paper offers a comprehensive proof of Handelman's theorem within the context of order unit normed spaces, clarifying the conditions under which such spaces are Banach.

Findings

Monotone sigma-complete order unit normed spaces are Banach spaces.

Detailed proof of Handelman's theorem provided.

Clarifies the relationship between order completeness and Banach space structure.

Abstract

We give a detailed proof D. Handelman's theorem stating (in the context of an order unit normed space) that a monotone sigma-complete order unit normed space is a Banach space.