The normality of macrocubes and hyperballeans

2020/05/29 by Igor Protasov, Protasov, Igor, Ksenia Protasova +1
Mathematics · #FOS: Mathematics #General Topology (math.GN) #math.GN

paper · pdf · doi:10.48550/arxiv.2006.00893

Keywords: coarse structure, ballean, macrocube, hyperballeans, Ramsey ultrafilter. Keywords: coarse structure, ballean, macrocube, hyperballeans, Ramsey ultrafilter

arxiv created 2020/07/01 · arxiv updated 2020/07/02

Abstract

For a bornology \mathcal B on a cardinal κ, we prove that the \mathcal B-macrocube is normal if and only if \mathcal B has a linearly ordered base. As a corollary, we get that the hyperballean of bounded subsets of an ultradiscrete ballean is not normal. These answer Question 1 from \citeb2 and Question 14.4 from \citeb1.

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