Both compact and sequentially compact sets in Abelian topological group
The authors consider convergent series in Abelian topological groups. They prove several technical results which make it possible to establish the following fact: if \(G\) is a Hausdorff Abelian topological group and a function \(\mu: 2^\omega\to G\) is countably additive, then its range \(\{\mu(A): A\in 2^\omega\}\) is compact and metrizable. Here \(2^\omega=\{A:A\subset \omega\}\). The developed techniques are also used to obtain some results on relative compactness in locally convex spaces.
scientific article; zbMATH DE number 5918213