On feebly compact inverse primitive (semi)topological semigroups

Abstract

We study the structure of inverse primitive pseudocompact semitopological and topologi- cal semigroups. We nd conditions when the maximal subgroup of an inverse primitive pseudocompact semitopological semigroupS is a closed subset ofS and describe the topological structure of such semireg- ular semitopological semigroups. Later we describe the structure of pseudocompact topological Brandt 0 -extensions of topological semigroups and semiregular (quasi-regular) primitive inverse topological semigroups. In particular we show that inversion in a quasi-regular primitive inverse pseudocompact topological semigroup is continuous. Also an analogue of Comfort{Ross Theorem proved for such semi- groups: a Tychono product of an arbitrary family of primitive inverse semiregular pseudocompact semitopological semigroups with closed maximal subgroups is pseudocompact. We describe the structure of the Stone- Cech compactication of a Hausdor primitive inverse countably compact semitopological semigroup S such that every maximal subgroup of S is a topological group.