Ideals in P _G and βG

2017/04/08 by Ігор Протасов, Protasov, Igor, Ksenia Protasova +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1704.02494

openalex publication_date 2017/04/08 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

For a discrete group G, we use the natural correspondence between ideals in the Boolean algebra P_G of subsets of G and closed subsets in the Stone-\checkCech compactifi-cation βG as a right topological semigroup to introduce and characterize some new ideals in βG. We show that if a group G is either countable or Abelian then there are no closed ideals in βG maximal in G^*, G^* = βG ∖ G, but this statement does not hold for the group S_κ of all permutations of an infinite cardinal κ. We characterize the minimal closed ideal in βG containing all idempotents of G^*.

Citations

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