English

Chain intersection closures

Logic 2021-08-25 v1 General Topology

Abstract

We study spherical completeness of ball spaces and its stability under expansions. We introduce the notion of an ultra-diameter, mimicking diameters in ultrametric spaces. We prove some positive results on preservation of spherical completeness involving ultra-diameters with values in narrow partially ordered sets. Finally, we show that in general, chain intersection closures of ultrametric spaces with partially ordered value sets do not preserve spherical completeness.

Keywords

Cite

@article{arxiv.1810.05832,
  title  = {Chain intersection closures},
  author = {Wieslaw Kubiś and Franz-Viktor Kuhlmann},
  journal= {arXiv preprint arXiv:1810.05832},
  year   = {2021}
}

Comments

11 pages

R2 v1 2026-06-23T04:38:29.669Z