On the interplay between productively Menger and productively Hurewicz spaces in models of $\mathfrak b=\mathfrak d$

Dušan D. Repovš; Lyubomyr Zdomskyy

doi:10.1016/j.topol.2025.109372

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arXiv · 2503.17969

On the interplay between productively Menger and productively Hurewicz spaces in models of $\mathfrak b=\mathfrak d$

Dušan D. Repovš·Lyubomyr Zdomskyy

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Abstract

This article is devoted to the interplay between productively Menger and productively Hurewicz subspaces of the Cantor space. In particular, we show that in the Laver model for the consistency of the Borel's conjecture these two notions coincide and characterize Hurewicz spaces. On the other hand, it is consistent with CH that there are productively Hurewicz subspaces of the Cantor space which are not productively Menger.

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Dušan D. Repovš, Lyubomyr Zdomskyy. 2025-03-23. On the interplay between productively Menger and productively Hurewicz spaces in models of $\mathfrak b=\mathfrak d$. https://doi.org/10.1016/j.topol.2025.109372

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