The Cartesian product of any family of $W$-spaces is $κ$-Fréchet-Urysohn

Mikołaj Krupski; Kacper Kucharski

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arXiv · 2608.11105

The Cartesian product of any family of $W$-spaces is $κ$-Fréchet-Urysohn

Mikołaj Krupski·Kacper Kucharski

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Abstract

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.

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BibTeX RIS

Mikołaj Krupski, Kacper Kucharski. 2026-08-11. The Cartesian product of any family of $W$-spaces is $κ$-Fréchet-Urysohn. https://arxiv.org/abs/2608.11105

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