The normality of macrocubes and hyperballeans
General Topology
2020-07-02 v2
Abstract
For a bornology on a cardinal , we prove that the -macrocube is normal if and only if 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 \cite{b2} and Question 14.4 from \cite{b1}.
Cite
@article{arxiv.2006.00893,
title = {The normality of macrocubes and hyperballeans},
author = {Igor Protasov and Ksenia Protasova},
journal= {arXiv preprint arXiv:2006.00893},
year = {2020}
}
Comments
Keywords: coarse structure, ballean, macrocube, hyperballeans, Ramsey ultrafilter. Keywords: coarse structure, ballean, macrocube, hyperballeans, Ramsey ultrafilter