关于Collins-Roscoe结构化机制的注记
A note on Collins-Roscoe Structuring Mechanism
摘要：
一个空间$X$具有可数$(F)$ -性质，如果它具有满足Collins-Roscoe结构机制的可数点网络.得到了$C_p(X)$具有可数$(F)$ -性质的一些充分条件.作为推论，我们证明了如果$X$是Corson紧的，则$C_p(X)$满足可数$(F)$ .这回答了Tkachuk提出的一个问题。并得到了一类具有遗传$D$ -性质的函数空间。我们还证明了取$Σ_s$-积保持了可列$(F)$ -性质。这肯定地回答了Tkachuk的问题。
英文摘要：
A space $X$ has countable $(F)$-property if it has countable point network satisfying the Collins-Roscoe structuring mechanism. Some sufficient conditions for $C_p(X)$ having countable $(F)$-property are obtained. As a corollary, we prove that if $X$ is Corson compact, $C_p(X)$ satisfies countable $(F)$. This answers a question raised by Tkachuk. Also we get a class of function spaces with hereditarily $D$-property. We also prove that the countable $(F)$-property is preserved by taking $Σ_s$-product. This answers questions of Tkachuk positively.
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。
