A note on quasi-Menger and similar spaces

Recently, several papers on weaker forms of classical covering properties of Menger, Hurewicz and Rothberger have been published. We complement this investigation studying new weak versions of these properties. Our study is related to selective versions of the quasi-Lindelöf property introduced in 1979 by A.V. Arhangel'skii. For example, we define quasi-Menger spaces and show that they are different from other weak versions of Menger's property.