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We construct Menger subsets of the real line whose product is not Menger in the plane. In contrast to earlier constructions, our approach is purely combinatorial. The set theoretic hypothesis used in our construction is far milder than earlier ones, and holds in all but the most exotic models of real set theory. On the other hand, we establish productive properties f
We study products of general topological spaces with Mengers covering property, and its refinements based on filters and semifilters. To this end, we extend the projection method from the classic real line topology to the Michael topology. Among othe
We construct, using mild combinatorial hypotheses, a real Menger set that is not Scheepers, and two real sets that are Menger in all finite powers, with a non-Menger product. By a forcing-theoretic argument, we show that the same holds in the Blass--
W. Hurewicz proved that analytic Menger sets of reals are $sigma$-compact and that co-analytic completely Baire sets of reals are completely metrizable. It is natural to try to generalize these theorems to projective sets. This has previously been ac
Which Isbell--Mrowka spaces ($Psi$-spaces) satisfy the star version of Mengers and Hurewiczs covering properties? Following Bonanzinga and Matveev, this question is considered here from a combinatorial point of view. An example of a $Psi$-space that
We provide conceptual proofs of the two most fundamental theorems concerning topological games and open covers: Hurewiczs Theorem concerning the Menger game, and Pawlikowskis Theorem concerning the Rothberger game.