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On a generalization of Abelian sequential groups

Saak S. Gabriyelyan — 2013

Fundamenta Mathematicae

Let (G,τ) be a Hausdorff Abelian topological group. It is called an s-group (resp. a bs-group) if there is a set S of sequences in G such that τ is the finest Hausdorff (resp. precompact) group topology on G in which every sequence of S converges to zero. Characterizations of Abelian s- and bs-groups are given. If (G,τ) is a maximally almost periodic (MAP) Abelian s-group, then its Pontryagin dual group ${(G, τ)}^{\land}$ is a dense -closed subgroup of the compact group ${(G_{d})}^{\land}$ , where $G_{d}$ is the group G with the discrete...

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