  We look at the Bohr topology of maximally almost periodic groups (MAP, for
short). Among other results, we investigate when a totally bounded 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 $w$. As an application, an example of a MAP group $(G,t)$ is
given such that every closed, metrizable subgroup $N$ of $bG$ with $N \cap G =
\{0\}$ preserves compactness but $(G,t)$ does not strongly respects
compactness. Thereby, we respond to Questions 4.1 and 4.3 in [comftrigwu].
