0505504 - MÚ 2020 RIV NL eng J - Journal Article
Kubiś, Wieslaw - Kuhlmann, F.-V.
Chain intersection closures.
Topology and its Applications. Roč. 262, 1 August (2019), s. 11-19. ISSN 0166-8641. E-ISSN 1879-3207
R&D Projects: GA ČR(CZ) GA17-27844S
Institutional support: RVO:67985840
Keywords : Ball space * spherical completeness * narrow poset * ultrametric
OECD category: Pure mathematics
Impact factor: 0.531, year: 2019
Method of publishing: Limited access
Result website:
http://dx.doi.org/10.1016/j.topol.2019.05.009
DOI: https://doi.org/10.1016/j.topol.2019.05.009

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.

Permanent Link: http://hdl.handle.net/11104/0296988