2020/07/11 by A Sergio, A, Sergio, Garcia-Balan +2
Mathematics · #54D15 (Primary) 54G20 (Secondary) #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2007.05844
openalex publication_date 2020/07/11 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
Almost disjoint families of true cardinality \mathfrakc are used to produce an example of a mildly-normal not partly-normal Ψ-space and a quasi-normal not almost-normal Ψ-space. This is related with a problem posed by Lufti Kalantan where he asks whether there exists a mad family so that the related Mrówka-Isbell space is partly-normal. In addition, a consistent example of a Luzin mad family such that its associated Ψ-space is quasi-normal is provided.