Large Sets in Boolean and Non-Boolean Groups and Topology

Abstract

Various notions of large sets in groups, including the classical notions of thick, syndetic, and piecewise syndetic sets and the new notion of vast sets in groups, are studied with emphasis on the interplay between such sets in Boolean groups. Natural topologies closely related to vast sets are considered; as a byproduct, interesting relations between vast sets and ultrafilters are revealed.

Keywords

• large set in a group
• vast set
• syndetic set
• thick set
• piecewise syndetic set
• Boolean topological group
• arrow ultrafilter
• Ramsey ultrafilter