Pontryagin duality for Abelian s- and sb-groups

2011/01/14 by Saak Gabriyelyan, S. S. Gabriyelyan, Gabriyelyan, S. S.
Computer Science · Mathematics · #22A10 #22A35 #43A05 #43A40 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #Mathematical Analysis and Transform Methods #math.FA #math.GR #msc:22A10 #msc:22A35 #msc:43A05 #msc:43A40

paper · pdf · doi:10.48550/arxiv.1101.2756

arxiv created 2011/01/14 · openalex publication_date 2011/01/14 · arxiv updated 2011/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main goal of the article is to study the Pontryagin duality for Abelian s- and sb-groups. Let G be an infinite Abelian group and X be the dual group of the discrete group G_d. We show that a dense subgroup H of X is \mathfrakg-closed iff H algebraically is the dual group of G endowed with some maximally almost periodic s-topology. Every reflexive Polish Abelian group is \mathfrakg-closed in its Bohr compactification. If a s-topology τ on a countably infinite Abelian group G is generated by a countable set of convergent sequences, then the dual group of (G,τ) is Polish. A non-trivial Hausdorff Abelian topological group is a s-group iff it is a quotient group of the s-sum of a family of copies of (ℤ^ℕ₀, e).

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