  In this short note, we give some new results on continuous bounded cohomology
groups of topological semigroups with values in complex field. We show that the
second continuous bounded cohomology group of a compact metrizable semigroup,
is a Banach space. Also, we study cohomology groups of amenable topological
semigroups, and we show that cohomology groups of rank greater than one of a
compact left or right amenable semigroup, are trivial. Also, we give some
examples and applications about topological lattices.
