Completeness for vector lattices

TL;DR

This paper investigates the concept of unbounded order convergence in vector lattices, establishing that universal completeness is equivalent to unbounded order completeness, and also explores the notion of sup-completion introduced by Donner.

Contribution

It proves the equivalence between universal completeness and unbounded order completeness in vector lattices, and discusses the notion of sup-completion.

Findings

Universal completeness iff unbounded order completeness in vector lattices

Unbounded order convergence is a significant and efficient concept

Analysis of Donner's sup-completion in the context of vector lattices

Abstract

The notion of unboundedly order converges has been recieved recently a particular attention by several authors. The main result of the present paper shows that the notion is efficient and deserves that care. It states that a vector lattice is universally complete if and only if it is unboundedly order complete. Another notion of completeness will be treated is the notion of sup-completion introduced by Donner.