On topological Brandt semigroups

We describe the structure of pseudocompact completely 0-simple topological inverse semigroups. As a consequence of this result the analogue of Comfort-Ross theorem for topological semigroups is obtained. We present also the sufficient conditions on topological Brandt extensions for preserving the (absolute) H-closedness and some criteria for the (absolute) H-closedness of topological Brandt semigroups.