Productive Lindelöfness and a class of spaces considered by Z. Frolík

We prove that closed subspaces of countable products of σ-compact spaces are productively Lindelöf if and only if there are no Michael spaces. We also prove that, assuming CH, if X is productively Lindelöf and the union of ℵ1 compact sets, then Xω is Lindelöf.