2023/11/15 by C.J. Griffin, Griffin, Conner
Computer Science · Mathematics · #22A15 #54D80 #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Rings, Modules, and Algebras #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2311.09436
openalex publication_date 2023/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Some filter relative notions of size, ( F,G) -syndeticity and piecewise F -syndeticity, were defined and applied with clarity and focus by Shuungula, Zelenyuk and Zelenyuk in their paper ``The closure of the smallest ideal of an ultrafilter semigroup.'' These notions are generalizations of the well studied notions of syndeticity and piecewise syndeticity. Since then, there has been an effort to develop the theory around the algebraic structure of the Stone-Čech compactification so that it encompasses these new generalizations. In this direction, we prove a characterization of piecewise F-syndetic sets. This fully answers a conjecture of Christopherson and Johnson. arXiv:2105.09723