Submission date: 13 October 2018

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.

Mathematics Subject Classification: 06A06, 54A05

Keywords and phrases:

Full text arXiv 1810.05832: pdf, ps.