遗传可分的薄-很高紧散布空间
Thin-very tall compact scattered spaces which are hereditarily separable
摘要：
我们加强属性$Δ$的功能$f:[ω_2]^2\rightarrow [ω_2]^{\leq ω}$考虑Baumgartner和Shelah。这使我们能够考虑在Rabus、Juhász和Soukup所使用的强迫中的新类型的合并，以构建薄而高的紧凑分散空间。我们一致地得到了空间$K$，其中$K^n$对于每个$n\in\N$是遗传可分的。这是一个关于紧空间上的基数函数的反例，在巴拿赫空间中也有一些应用：Banach空间$C(K)$是一个密度为$\aleph_2$的Asplund空间，它没有Fréchet光滑重赋范，也没有不可数的双正交系。
英文摘要：
We strengthen the property $Δ$ of a function $f:[ω_2]^2\rightarrow [ω_2]^{\leq ω}$ considered by Baumgartner and Shelah. This allows us to consider new types of amalgamations in the forcing used by Rabus, Juhász and Soukup to construct thin-very tall compact scattered spaces. We consistently obtain spaces $K$ as above where $K^n$ is hereditarily separable for each $n\in\N$. This serves as a counterexample concerning cardinal functions on compact spaces as well as having some applications in Banach spaces: the Banach space $C(K)$ is an Asplund space of density $\aleph_2$ which has no Fréchet smooth renorming, nor an uncountable biorthogonal system.
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