Ultracompanions of subsets of a group

2013/08/07 by Ігор Протасов, Protasov, I., Serhii Slobodianiuk +1 · 1 citation
Mathematics · #20F69 #22A15 #54D35 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1308.1499

openalex publication_date 2013/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a group, βG is the Stone-\checkCech compactification of βG endowed with the structure of a right topological semigroup, G^*=βG∖ G. Given any subset A of G and p∈ G^*, we define the p-companion \vt_p(A)=A^*∩ Gp of A, and characterize the subsets with finite and discrete ultracompanions.

Citations

• Asymptotically Scattered Spaces

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• Ideals in P _G and βG

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