English

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 XX is not topological unless dimX<\dim X<\infty. 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}
}
R2 v1 2026-06-22T20:01:16.026Z