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arXiv · 1810.05832

Chain intersection closures

Wieslaw Kubiś·Franz-Viktor Kuhlmann
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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.

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Wieslaw Kubiś, Franz-Viktor Kuhlmann. 2018-10-13. Chain intersection closures. https://doi.org/10.1016/j.topol.2019.05.009

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