Order convergence in infinite-dimensional vector lattices is not topological
Functional Analysis
2017-05-30 v1
Abstract
In this note, we show that the order convergence in a vector lattice is not topological unless . Furthermore, we show that, in atomic order continuous Banach lattices, the order convergence is topological on order intervals.
Keywords
Cite
@article{arxiv.1705.09883,
title = {Order convergence in infinite-dimensional vector lattices is not topological},
author = {Y. A. Dabboorasad and E. Y. Emelyanov and M. A. A. Marabeh},
journal= {arXiv preprint arXiv:1705.09883},
year = {2017}
}