Remarks on set-Menger and related properties

In this note we prove that the set-Menger, set-Hurewicz and set-Rothberger properties, recently introduced in [1], are actually another view of the Menger, Hurewicz and Rothberger properties, while the weakly set-Menger and weakly set-Rothberger properties are another view of quasi-Menger and quasi-Rothberger properties [2], respectively. We also prove that the almost set-Menger property in is different from the quasi-Menger property. Problem 4.20 from [1] is addressed. (C) 2020 Elsevier B.V. All rights reserved.