Luzin和反Luzin几乎不相交族

$Ψ$-空间与半近邻性

$Ψ$-Spaces and Semi-Proximality

本文研究了$Ψ$-空间中的半近邻性，证明了几乎不相交族和梯系统下半近邻性的特征，并得出非半近邻$Ψ$-空间的存在性独立于ZFC的结论。

On $\mathbb R$-embeddability of almost disjoint families and Akemann-Doner C*-algebras

An almost disjoint family $\mathcal A$ of subsets of $\mathbb N$ is said to be $\mathbb R$-embeddable if there is a function $f:\mathbb N\rightarrow \mathbb R$ such that the sets $f[A]$ are ranges of real sequences converging to distinct reals for distinct $A\in \mathcal A$. It is well known that almost disjoint families which have few separations, such as Luzin families, are not $\mathbb R$-embeddable. We study extraction principles related to $\mathbb R$-embeddability and separation properties of almost disjoint families of $\mathbb N$ as well as their limitations. An extraction principle wh…

几乎不相交族和一些自同构和单射性质的ℓ∞/c₀

Almost disjoint families and some automorphic and injective properties of $\ell_\infty/c_0$

本文研究了ℓ∞/c₀中几乎不相交族的自同构和单射性质，证明在ZFC下某些陈述独立，并展示了正负一致性结果。