On almost disjoint families and Johnson-Lindenstrauss spaces

Antonio Avilés; Grzegorz Plebanek; Luis Sáenz

paper

On almost disjoint families and Johnson-Lindenstrauss spaces

arXiv:2607.13214

Abstract

Every almost disjoint family $A$ of infinite subsets of $ω$ gives rise to a scattered compact space $K_{A}$ and a family of Johnson-Lindenstrauss spaces JL $_{p} (A)$ . We consider almost disjoint families arising from finitely branching trees and investigate whether they define homeomorphic compacta and isomorphic Banach spaces.

19 pages, first version