Products of general Menger spaces
Piotr Szewczak, Boaz Tsaban

TL;DR
This paper investigates how Menger's covering property behaves under products of topological spaces, extending existing methods and establishing implications under the Continuum Hypothesis.
Contribution
It extends the projection method to the Michael topology and proves new implications between productively Lindelöf, Menger, and Hurewicz spaces under CH.
Findings
Under CH, every productively Lindelöf space is productively Menger.
Under CH, every productively Menger space is productively Hurewicz.
Implications between these properties are not reversible.
Abstract
We study products of general topological spaces with Menger's 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 other results, we prove that, assuming \CH{}, every productively Lindel\"of space is productively Menger, and every productively Menger space is productively Hurewicz. None of these implications is reversible.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
