  An action of a group $G$ on a compact space $X$ is called weakly almost
periodic if the orbit of every continuous function on $X$ is weakly relatively
compact in $C(X)$. We observe that for a topological group $G$ the following
are equivalent: (i) every continuous action of $G$ on a compact space is weakly
almost periodic; (ii) $G$ is precompact. For monothetic groups the result was
previously obtained by Akin and Glasner, while for locally compact groups it
has been known for a long time.
