  We detect topological semigroups that are topological paragroups, i.e., are
isomorphic to a Rees product of a topological group over topological spaces
with a continuous sandwich function. We prove that a simple topological
semigroup $S$ is a topological paragroup if one of the following conditions is
satisfied: (1) $S$ is completely simple and the maximal subgroups of $S$ are
topological groups, (2) $S$ contains an idempotent and the square $S\times S$
is countably compact or pseudocompact, (3) $S$ is sequentially compact or each
power of $S$ is countably compact. The last item generalizes an old Wallace's
result saying that each simple compact topological semigroup is a topological
paragroup.
