A density counterpart of the Scheepers covering property

Abstract

We introduce a density counterpart of the Scheepers covering property ${\bigcup }_{\mathrm{fin}}(\mathcal{O},\Omega )$ and study its relations to known combinatorial density property. In particular, we show that it is equivalent to the $M$-separability under the Near Coherence of Filters principle of Blass and Weiss.