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

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.

References in corpus (2)

• A semifilter approach to selection principles
• Products of Hurewicz spaces in the Laver model