Products of Hurewicz, Menger and Lindelof spaces

We consider products of general topological spaces with Hurewicz’s, Menger’s and Lindelof’s covering properties. Assuming the Continuum Hypothesis, we prove that every productively Lindelof space is productively Menger, and every productively Menger space is productively Hurewicz. We also provide examples that none of these implications is reversible. The above results generalize earlier results of Aurichi-Tall and Repovs-Zdomskyy for general topological spaces and results of Miller-Tsaban-Zdomskyy for hereditarily Lindelof spaces.  This is a joint work with Boaz Tsaban.