2021/12/18 by Vinicius de Oliveira Rodrigues, Rodrigues, Vinicius, Victor dos Santos Ronchim +3
Mathematics · #54D15 #54D80 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2112.09830
openalex publication_date 2021/12/18 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
We recall some classical results relating normality and some natural weakenings of normality in Ψ-spaces over almost disjoint families of branches in the Cantor tree to special sets of reals like Q-sets, λ-sets and σ-sets. We introduce a new class of special sets of reals which corresponds the corresponding almost disjoint family of branches being ℵ0-separated. This new class fits between λ-sets and perfectly meager sets. We also discuss conditions for an almost disjoint family \mathcal A being potentially almost-normal (pseudonormal), in the sense that \mathcal A is almost-normal (pseudonormal) in some c.c.c. forcing extension.