Products of Menger spaces in the Miller model

TL;DR

This paper proves that in the Miller model, the Menger property remains intact under finite products of metrizable spaces, highlighting the relationship between forcing techniques and topological covering properties.

Contribution

It demonstrates that the Menger property is preserved under finite products in the Miller model, addressing open questions in topology and forcing.

Findings

Menger property preserved in the Miller model

Finite products of metrizable spaces retain the Menger property

Connects forcing posets with combinatorial covering properties

Abstract

We prove that in the Miller model the Menger property is preserved by finite products of metrizable spaces. This answers several open questions and gives another instance of the interplay between classical forcing posets with fusion and combinatorial covering properties in topology.