Embedded unbounded order convergent sequences in topologically convergent nets in vector lattices
Functional Analysis
2024-03-25 v2
Abstract
We show that, for a class of locally solid topologies on vector lattices, a topologically convergent net has an embedded sequence that is unbounded order convergent to the same limit. Our result implies, and often improves, many of the known results in this vein in the literature. A study of metrisability and submetrisability of locally solid topologies on vector lattices is included.
Cite
@article{arxiv.2309.03027,
title = {Embedded unbounded order convergent sequences in topologically convergent nets in vector lattices},
author = {Yang Deng and Marcel de Jeu},
journal= {arXiv preprint arXiv:2309.03027},
year = {2024}
}
Comments
25 pages. Proposition 3.7 has been strengthened. Final version, to appear in Banach J. Math. Anal