Remarks on the preservation of topological covering properties under Cohen forcing

TL;DR

This paper proves that certain topological covering properties, including Rothberger, Menger, and selective screenability, are preserved under Cohen forcing and measure algebra forcing, extending previous results.

Contribution

The paper improves upon Iwasa's argument to show that multiple covering properties are preserved under Cohen and measure algebra forcing.

Findings

Rothberger property is preserved under Cohen forcing.

Menger property is preserved under Cohen forcing.

Selective screenability is preserved under Cohen forcing.

Abstract

Iwasa investigated the preservation of various covering properties of opological spaces under Cohen forcing. By improving the argument in Iwasa's paper, we prove that the Rothberger property, the Menger property and selective screenability are also preserved under Cohen forcing and forcing with the measure algebra.