伪径向空间和$ω_1+1$的副本
Pseudoradial spaces and copies of $ω_1+1$
摘要：
本文在紧空间的范围内比较了伪径向空间和最近定义的强伪径向空间的概念。我们证明了$\mathrm{MA}+\mathfrak{c}=ω_2$蕴含着存在一个紧的伪径向空间，它不是强伪径向的。我们本质上构造了一个紧的，序列紧的空间$X$和一个连续函数$f:X\toω_1+1$，使得在$X$中没有$ω_1+1$的副本，它映射到$f$下的共尾。我们还给出了空间中存在$ω_1$拷贝的条件。特别是，$\mathrm{PFA}$意味着紧几乎径向空间的径向字符$ω_1$包含许多副本的$ω_1$。
英文摘要：
In this paper we compare the concepts of pseudoradial spaces and the recently defined strongly pseudoradial spaces in the realm of compact spaces. We show that $\mathrm{MA}+\mathfrak{c}=ω_2$ implies that there is a compact pseudoradial space that is not strongly pseudoradial. We essentially construct a compact, sequentially compact space $X$ and a continuous function $f:X\toω_1+1$ in such a way that there is no copy of $ω_1+1$ in $X$ that maps cofinally under $f$. We also give some conditions that imply the existence of copies of $ω_1$ in spaces. In particular, $\mathrm{PFA}$ implies that compact almost radial spaces of radial character $ω_1$ contain many copies of $ω_1$.
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