English

A counterexample regarding the relatively uniform completion of a principal ideal

Commutative Algebra 2025-06-12 v1 Functional Analysis

Abstract

We present a counterexample related to relative uniform convergence, showing that, in general, the relatve uniform completion of the principal ideal of a vector lattice E generated by an element x is stricly contained in the ideal generated by x in the relatively uniform completion of E.

Keywords

Cite

@article{arxiv.2506.09798,
  title  = {A counterexample regarding the relatively uniform completion of a principal ideal},
  author = {Youssef Azouzi},
  journal= {arXiv preprint arXiv:2506.09798},
  year   = {2025}
}