On almost disjoint families and Johnson-Lindenstrauss spaces
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.
Disclosure
“esides the facts mentioned in this introduction, other finer but more technical results are included along the text. Finally, Section 7 lists some open problems. The main ideas used in this article were found by the authors. We used AI (Chatgpt 5.5) to revise and improve earlier versions of the work.”
PDF page 2
- Classification
- Substantial mathematical content or result generation
- Multiplier
- 10
- Verified
Structural counts
Pages 19 pdf
Theorems 9 source
Lemmas 9 source
Propositions 0 source
Corollaries 2 source
Definitions 2 source
Displayed equations 95 source
Bibliography entries 51 source
Appendix pages 0 estimated
Count notes
- Source counts use the expanded primary TeX file jl_ver_arxiv.tex.
- Appendix pages include the first PDF page with an explicit Appendix heading through the final page.