Factoring groups into dense subsets

2016/02/04 by Ігор Протасов, Igor Protasov, Protasov, Igor +2
Decision Sciences · Mathematics · #20A05 #22A05 #Advanced Topology and Set Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #Group Theory (math.GR) #Rings, Modules, and Algebras #math.GR #msc:20A05 #msc:22A05

paper · pdf · doi:10.48550/arxiv.1602.01603

arxiv created 2016/02/04 · openalex publication_date 2016/02/04 · arxiv updated 2016/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a group of cardinality κ>ℵ₀ endowed with a topology τ such that |U|=κ for every non-empty U∈τ and τ has a base of cardinality κ. We prove that G could be factorized G=AB (i.e. each g∈ G has unique representation g=ab, a∈ A, b∈ B) into dense subsets A,B, |A|=|B|=κ. We do not know if this statement holds for κ= ℵ₀ even if G is a topological group.

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