English

The normality of macrocubes and hyperballeans

General Topology 2020-07-02 v2

Abstract

For a bornology B\mathcal B on a cardinal κ\kappa, we prove that the B\mathcal B-macrocube is normal if and only if B\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 \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

R2 v1 2026-06-23T15:57:37.012Z