Some properties of the ideal of nowhere dense sets in the common division topology

Abstract

We consider the ideal of nowhere dense sets in the common division topology (Szyszkowska’s ideal), and examine some of its basic properties. We also explore the possible inclusions between the studied ideal and Furstenberg’s and Rizza’s ideals, thus answering open questions posed in a recent article by A. Nowik and P. Szyszkowska [17]. Moreover, we discuss the relationships of the Szyszkowska’s ideal with selected well-known ideals playing an important role in number theory and combinatorics.