Isbell-Mrówka空间上的特殊实集与弱正规型
Special sets of reals and weak forms of normality on Isbell-Mrówka spaces
摘要：
我们回顾了一些经典的结果有关的正规性和一些自然削弱的正规性$Ψ$ -空间的几乎不相交的家庭的分支在康托树的特殊集的实数，如$Q$ -集，$λ$ -集和$σ$ -集。我们引入一类新的特殊实数集，它对应于几乎不相交的分支族是$\aleph_0$ -分离的。这个新类适合于$λ$ -集和完全贫乏集之间。我们还讨论了一个几乎不相交的家庭$\mathcal A$潜在的几乎正常（正态）的条件，在这个意义上，$\mathcal A$是几乎正常（正态）在一些c.c.c.力迫扩张。
英文摘要：
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 $\aleph_0$-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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
