论文标题
lindelöf散落的空间
First-countable Lindelöf scattered spaces
论文作者
论文摘要
我们研究了一类可容纳的Lindelöf散射空间或“ FLS”空间。虽然每个$ t_3 $ fls空间都是$ \ mathbb Q $的分散子空间的同型，但$ T_2 $ fls的班级却令人惊讶地富裕。我们对这些空间的调查揭示了与$ q $ - 集，卢辛集合及其亲戚的紧密联系，以及红衣主教$ \ mathfrak {b} $和$ \ mathfrak {d} $。关于FLS空间的许多自然问题结果与$ \ Mathsf {ZFC} $无关。 我们证明存在具有散射高度$ω$的无数fl空间。另一方面，当且仅当$ \ mathfrak {b} = \ aleph_1 $时，就存在一个无限散射高度的空间。我们证明了有关FLS空间可能的基础性的一些独立性结果，以及关于哪些序数可能是FLS空间的散射高度。包括几个开放问题。
We study the class of first-countable Lindelöf scattered spaces, or "FLS" spaces. While every $T_3$ FLS space is homeomorphic to a scattered subspace of $\mathbb Q$, the class of $T_2$ FLS spaces turns out to be surprisingly rich. Our investigation of these spaces reveals close ties to $Q$-sets, Lusin sets, and their relatives, and to the cardinals $\mathfrak{b}$ and $\mathfrak{d}$. Many natural questions about FLS spaces turn out to be independent of $\mathsf{ZFC}$. We prove that there exist uncountable FLS spaces with scattered height $ω$. On the other hand, an uncountable FLS space with finite scattered height exists if and only if $\mathfrak{b} = \aleph_1$. We prove some independence results concerning the possible cardinalities of FLS spaces, and concerning what ordinals can be the scattered height of an FLS space. Several open problems are included.
