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Large Sets in Boolean and Non-Boolean Groups and Topology

Department of General Topology and Geometry, Lomonosov Moscow State University, Leninskie Gory 1, Moscow 119991, Russia
Axioms 2017, 6(4), 28; https://doi.org/10.3390/axioms6040028
Received: 1 September 2017 / Revised: 20 October 2017 / Accepted: 23 October 2017 / Published: 24 October 2017
(This article belongs to the Collection Topological Groups)
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. View Full-Text
Keywords: large set in a group; vast set; syndetic set; thick set; piecewise syndetic set; Boolean topological group; arrow ultrafilter; Ramsey ultrafilter large set in a group; vast set; syndetic set; thick set; piecewise syndetic set; Boolean topological group; arrow ultrafilter; Ramsey ultrafilter
MDPI and ACS Style

Sipacheva, O.V. Large Sets in Boolean and Non-Boolean Groups and Topology. Axioms 2017, 6, 28.

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