The pseudometric topology induced by upper asymptotic density
General Topology
2024-10-10 v1 Logic
Abstract
Upper asymptotic density induces a pseudometric on the power set of the natural numbers, with respect to which is complete. The collection of sets with asymptotic density is closed in this pseudometric, and closed subsets of are characterised by a generalisation of an additivity property (AP0).
Cite
@article{arxiv.2410.06559,
title = {The pseudometric topology induced by upper asymptotic density},
author = {Jonathan M. Keith},
journal= {arXiv preprint arXiv:2410.06559},
year = {2024}
}