We use Ramseyan partition relations to characterize: ∙ the classical covering property of Hurewicz; ∙ the covering property of Gerlits and Nagy; ∙ the combinatorial cardinal numbers and add(ℳ ). Let X be a -space. In [9] we showed that has countable strong fan tightness as well as the Reznichenko property if, and only if, all finite powers of X have the Gerlits-Nagy covering property. Now we show that the following are equivalent: 1. has countable fan tightness and the Reznichenko property. 2. All finite powers of X have the Hurewicz property. We show that for the combination of countable fan tightness with the Reznichenko property is characterized by a Ramseyan partition relation. Extending the work in [9], we give an analogous Ramseyan characterization for the combination of countable strong fan tightness with the Reznichenko property on .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm179-2-2,
author = {Ljubi\v sa D. R. Ko\v cinac and Marion Scheepers},
title = {Combinatorics of open covers (VII): Groupability},
journal = {Fundamenta Mathematicae},
volume = {177},
year = {2003},
pages = {131-155},
zbl = {1115.91013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm179-2-2}
}
Ljubiša D. R. Kočinac; Marion Scheepers. Combinatorics of open covers (VII): Groupability. Fundamenta Mathematicae, Tome 177 (2003) pp. 131-155. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm179-2-2/