Abstract
We study, in a systematic manner, products of general topological spaces with Menger's covering property, and its refinements based on filters and semifilters. To this end, we apply Dedekind compactification to extend the projection method from the classic real line topology to the Michael topology. Among other results, we prove that, assuming the Continuum Hypothesis, every productively Lindelöf space is productively Menger, and every productively Menger space is productively Hurewicz. None of these implications is reversible.
| Original language | English |
|---|---|
| Pages (from-to) | 41-55 |
| Number of pages | 15 |
| Journal | Topology and its Applications |
| Volume | 255 |
| DOIs | |
| State | Published - 15 Mar 2019 |
Bibliographical note
Publisher Copyright:© 2019
Funding
We thank Arnold Miller for Lemma 3.16, and Franklin Tall for pointing out useful references. We thank the referee for a very detailed report. The research of the first named author was supported by an Etiuda 2 grant, Polish National Science Center, UMO-2014/12/T/ST1/00627. We thank Arnold Miller for Lemma 3.16 , and Franklin Tall for pointing out useful references. We thank the referee for a very detailed report. The research of the first named author was supported by an Etiuda 2 grant, Polish National Science Center , UMO-2014/12/T/ST1/00627 .
| Funders | Funder number |
|---|---|
| Polish National Science Center | UMO-2014/12/T/ST1/00627 |
| Narodowe Centrum Nauki |
Keywords
- Concentrated sets
- Hurewicz property
- Menger property
- Product spaces
- Productively Hurewicz
- Productively Lindelöf
- Productively Menger