When a totally bounded group topology is the Bohr topology of a LCA group

摘要

We look at the Bohr topology of maximally almost periodic groups (MAP, for short). Among other results, we investigate when a Hausdorff precompact abelian group (G, w) is the Bohr reflection of a locally compact abelian group. Necessary and sufficient conditions are established in terms of the inner properties of the topology w. As an application, an example of a MAP group (G, t) is given such that every closed, metrizable subgroup N of bG with N boolean AND G = {0} preserves compactness but (G, t) does not strongly respect compactness. Thereby, we respond to Questions 4.1 and 4.3 in [6]. (C) 2019 Elsevier B.V. All rights reserved.