论文标题
紧凑型空间，带有$ p $ bas
Compact Spaces with a $P$-base
论文作者
论文摘要
在论文中，我们调查了（分散的）紧凑型空间，其中某些poset $ p $ $ p $ bas。更具体地说，我们证明，在假设$ω_1<\ mathfrak {b} $下，任何具有$ω^ω$ - 基本的紧凑空间都是首先计算的，并且任何具有$ω^ω$ basase的散落的紧凑空间都是可计数的。这些为问题提供了积极的解决方案8.6.9和8.7.7在\ cite {banakh2019}中。使用强迫，我们还证明，在$ω_1<\ mathfrak {b} $的型号中，有一个不可首选的紧凑型空间，带有$ p $ - base，用于某些poset $ p $，带有口径〜$ω_1$。
In the paper, we investigate (scattered) compact spaces with a $P$-base for some poset $P$. More specifically, we prove that, under the assumption $ω_1<\mathfrak{b}$, any compact space with an $ω^ω$-base is first-countable and any scattered compact space with an $ω^ω$-base is countable. These give positive solutions to Problems 8.6.9 and 8.7.7 in \cite{Banakh2019}. Using forcing, we also prove that in a model of $ω_1<\mathfrak{b}$, there is a non-first-countable compact space with a $P$-base for some poset $P$ with calibre~$ω_1$.
