BRANDT EXTENSIONS AND PRIMITIVE TOPOLOGICALLY PERIODIC INVERSE TOPOLOGICAL SEMIGROUPS

We find sufficient conditions on primitive inverse topological semigroup S under which the inversion inv: (H(S))* → (H(S))* is continuous; we show that every topologically periodic countable compact primitive inverse topological semigroups with closed H-classes is topologically isomorphic to an orthogonal sum ∑ i element of ? Bλi (Gi) of topological Brandt λi-extensions Bλi (Gi) of countably compact topological groups Gi in the class of topological inverse semigroups, for some finite cardinals λi ≥ 1.