# Unbounded Order Convergence and Universal Completions

## TL;DR

This paper characterizes vector lattices where unbounded order convergence becomes order bounded, providing a solution to a previously posed problem and advancing the understanding of convergence properties in vector lattices.

## Contribution

It offers a new characterization of vector lattices with unbounded order convergence that is eventually order bounded, solving an open problem in the field.

## Key findings

- Characterization of vector lattices with unbounded order convergence
- Solution to Problem 23 in Azema's work
- Advancement in understanding convergence in vector lattices

## Abstract

We characterize vector lattices in which unbounded order convergence is eventually order bounded. Among other things, the characterization provides a solution to \cite[Probl.23]{Az}.