Preservation of $\gamma$-spaces and covering properties of products

TL;DR

This paper investigates how certain topological properties, specifically the Hurewicz property and $oldsymbol{ extgamma}$-spaces, behave under finite products within the Miller model, revealing that the Hurewicz property is not preserved.

Contribution

It demonstrates that Miller forcing preserves ground model $oldsymbol{ extgamma}$-spaces and shows the non-preservation of the Hurewicz property under finite products in this model.

Findings

Hurewicz property is not preserved by finite products in the Miller model.

Miller forcing preserves ground model $oldsymbol{ extgamma}$-spaces.

The result impacts understanding of product behavior of covering properties.

Abstract

We prove that the Hurewicz property is not preserved by finite products in the Miller model. This is a consequence of the fact that Miller forcing preserves ground model $\gamma$-spaces.