Locally compact abelian groups admitting non-trivial quasi-convex null sequences

2008/12/31 by Dikran Dikranjan, Dikranjan, Dikran, Gábor Lukács +1
Decision Sciences · Mathematics · #22A05 #22B05 #22C05 (Primary) #54H11 (Secondary) #Advanced Topology and Set Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.0901.0132

openalex publication_date 2008/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show that for every locally compact abelian group G, the following statements are equivalent: (i) G contains no sequence x_n such that 0 ∪ ± x_n : n ∈ N is infinite and quasi-convex in G, and x_n --> 0; (ii) one of the subgroups g ∈ G : 2g=0 and g ∈ G : 3g=0 is open in G; (iii) G contains an open compact subgroup of the form Z₂^κor Z₃^κfor some cardinal κ.

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