Brandt extensions and primitive topologically periodic inverse topological semigroups

Abstract

In this paper we find sufficient conditions on primitive inverse <br />topological semigroup S under which: the inversion inv : (H(S)) (H(S)) <br />is continuous; we show that every topologically periodic countable compact <br />primitive inverse topological semigroups with closed H-classes is topologically <br />isomorphic to an orthogonal sum <br />P <br />i2= Bi (Gi) of topological Brandt extensions Bi (Gi) of countably compact topological groups Gi in the class <br />of topological inverse semigroups for some finite cardinals.