Sequences suffice for pointfree uniform completions
General Topology
2025-09-29 v2
Abstract
Completions of metric spaces are usually constructed using Cauchy sequences. However, this does not work for general uniform spaces, where Cauchy filters or nets must be used instead. The situation in pointfree topology is more straightforward: the correct completion of uniform locales can indeed be obtained as a quotient of a locale of Cauchy sequences.
Cite
@article{arxiv.2409.15569,
title = {Sequences suffice for pointfree uniform completions},
author = {Graham Manuell},
journal= {arXiv preprint arXiv:2409.15569},
year = {2025}
}
Comments
17 pages, minor edits