关于Angelo Bella的一个问题
On a problem of Angelo Bella
摘要：
本文的主要结果是下面的定理。“如果$X$是任何具有$κ= \widehat{F}(X) \cdot \widehatμ(X)$的Hausdorff空间，则$L(X_{< κ}) \le \varrho(κ)$“。这里，$\widehat{F}(X)$是最小基数$φ$，使得对于$X$中自由的任何集合$S$，$\widehatμ(X)$是最小基数$μ$，使得对于$X$中自由的每个集合$S$，$\overline {S}$的任何开覆盖都具有大小为$< μ$的子覆盖。此外，$X_{< κ}$是$X$和$\varrho(κ) = \min \{\varrho : \varrho ^{< κ} = \varrho\}$的$G_{< κ}$ -修饰。作为推论，我们得到：如果$X$是可数紧性的线性Lindelöf正则空间，则$L(X_δ) \le \mathfrak{c}$，只要$ \mathfrak{c} = 2^{< \mathfrak{c}}$ .这产生了一个一致的肯定的答案安吉洛贝拉的问题。
英文摘要：
The main result of this note is the following theorem. "If $X$ is any Hausdorff space with $κ= \widehat{F}(X) \cdot \widehatμ(X)$ then $L(X_{< κ}) \le \varrho(κ)$". Here $\widehat{F}(X)$ is the smallest cardinal $φ$ so that $|S| < φ$ for any set $S$ that is free in $X$ and $\widehatμ(X)$ is the smallest cardinal $μ$ so that, for every set $S$ that is free in $X$, any open cover of $\overline {S}$ has a subcover of size $< μ$. Moreover, $X_{< κ}$ is the $G_{< κ}$-modification of $X$ and $\varrho(κ) = \min \{\varrho : \varrho ^{< κ} = \varrho\}$. As a corollary we obtain that if $X$ is a linearly Lindelöf regular space of countable tightness then $L(X_δ) \le \mathfrak{c}$, provided that $ \mathfrak{c} = 2^{< \mathfrak{c}}$. This yields a consistent affirmative answer to a question of Angelo Bella.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
