论文标题
拓扑空间和类似俱乐部的原则的隔断
Partitions of topological spaces and a new club-like principle
论文作者
论文摘要
我们给出了由于W. Weiss和P. Komjath引起的以下定理的新证明：如果$ x $是常规的拓扑空间，带有$ <\ mathfrak {b} $和$ x \ rightarrow（topω+ 1）^{1}_Ω_Ω$，那么，对于所有$α<ω_1$ x \ x \ righorow（top）在原始的。为此，我们考虑了拓扑空间的新分解。我们还定义了一个新的组合原理$ \ clubsuit_ {f} $，并用它来证明它与$ \ neg ch $一致，即$ \ mathfrak {b} $是$ x $的最佳限制。在\ cite {weisskomjath}中，这是使用$ \ diamondsuit $获得的。
We give a new proof of the following theorem due to W. Weiss and P. Komjath: if $X$ is a regular topological space, with character $ < \mathfrak{b}$ and $X \rightarrow (top ω+ 1)^{1}_ω$, then, for all $α< ω_1$, $X \rightarrow (top α)^{1}_ω$, fixing a gap in the original one. For that we consider a new decomposition of topological spaces. We also define a new combinatorial principle $\clubsuit_{F}$, and use it to prove that it is consistent with $\neg CH$ that $\mathfrak{b}$ is the optimal bound for the character of $X$. In \cite{WeissKomjath}, this was obtained using $\diamondsuit$.
