%0 Journal Article
%T On feebly compact inverse primitive (semi)topological semigroups
%A Oleg Gutik
%A Oleksandr Ravsky
%J Mathematics
%D 2013
%I arXiv
%X We study the structure of inverse primitive feebly compact semitopological and topological semigroups. We find conditions when the maximal subgroup of an inverse primitive feebly compact semitopological semigroup $S$ is a closed subset of $S$ and describe the topological structure of such semiregular semitopological semigroups. Later we describe the structure of feebly compact topological Brandt $\lambda^0$-extensions of topological semigroups and semiregular (quasi-regular) primitive inverse topological semigroups. In particular we show that inversion in a quasi-regular primitive inverse feebly compact topological semigroup is continuous. Also an analogue of Comfort--Ross Theorem is proved for such semigroups: a Tychonoff product of an arbitrary family of primitive inverse semiregular feebly compact semitopological semigroups with closed maximal subgroups is feebly compact. We describe the structure of the Stone-\v{C}ech compactification of a Hausdorff primitive inverse countably compact semitopological semigroup $S$ such that every maximal subgroup of $S$ is a topological group.
%U http://arxiv.org/abs/1310.4313v2