On feebly compact inverse primitive (semi)topological semigroups

O. Gutik, O. Ravsky
Faculty of Mathematics, Ivan Franko National University of Lviv, Pidstrygach Institute for Applied Problems of Mechanics and Mathematics of NASU
We study the structure of inverse primitive feebly compact semitopological and topological semigroups. We find conditions under which 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 the inversion in a quasi-regular primitive inverse feebly compact topological semigroup is continuous. An analogue of the Comfort--Ross Theorem is proved for such semigroups: the 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-Cech compactification of a Hausdorff primitive inverse countably compact semitopological semigroup~$S$ such that every maximal subgroup of $S$ is a topological group.
semigroup; primitive inverse semigroup; Brandt $\lambda^0$-extension; topological semigroup; topological group; paratopological group; semitopological semigroup; semitopological group; topological Brandt $\lambda^0$-extension; Brandt semigroup; primitive inverse semigroup; pseudocompact space; feebly compact space; countably compact space; countably pracompact space; Stone-Cech compactification
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