任意W-空间族的笛卡尔积是κ-Fréchet-Urysohn空间
The Cartesian product of any family of $W$-spaces is $κ$-Fréchet-Urysohn
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中文总结 AI 辅助
本文证明任意W-空间的乘积是κ-Fréchet-Urysohn空间，还给出乘积空间边界紧度的上界，部分解决Tkachuk提出的问题。
中文摘要 AI 辅助
本文证明，任意W-空间的乘积是κ-Fréchet-Urysohn空间；还证明，若X是紧空间且其紧度t(X)≤κ，Y的边界紧度tb(Y)≤κ，则乘积X×Y的边界紧度至多为κ。第一个结果完全解决了Tkachuk近期提出的两个问题，第二个结果部分解决了其中一个问题。
英文摘要
In this note, we prove that an arbitrary product of $W$-spaces is a $κ$-Fréchet-Urysohn space. We also show that the boundary tightness of a product $X \times Y$ is at most $κ$ provided that $X$ is compact with tightness $t(X) \leq κ$ and $Y$ has boundary tightness $tb(Y) \leq κ$. The first result fully resolves, and the second partially addresses, two questions recently raised by Tkachuk.
