Countability conditions in locally solid convergence spaces
Functional Analysis
2025-09-22 v2
Abstract
We study (strong) first countability of locally solid convergence structures on Archimedean vector lattices. Among other results, we characterise those vector lattices for which relatively unform-, order-, and -order convergence, respectively, is (strongly) first countable. The implications for the validity of sequential arguments in the contexts of these convergences are pointed out.
Cite
@article{arxiv.2501.11517,
title = {Countability conditions in locally solid convergence spaces},
author = {Eugene Bilokopytov and Viktor Bohdanskyi and Jan Harm van der Walt},
journal= {arXiv preprint arXiv:2501.11517},
year = {2025}
}
Comments
32 pages