On feebly compact inverse primitve (semi)topological semigroups

DOI10.15330/MS.44.1.3-26zbMATH Open1356.22002arXiv1310.4313OpenAlexW2964237867MaRDI QIDQ332240

O. Gutik, O. Ravsky

Publication date: 27 October 2016

Published in: Matematychni Studiï (Search for Journal in Brave)

Abstract: 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 $lambd{a}^0$-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.

Full work available at URL: https://arxiv.org/abs/1310.4313

zbMATH Keywords

semitopological semigrouptopological semigroupStone-Čech compactificationcountably compact spacepseudocompact spaceBrandt semigroupfeebly compact spaceprimitive inverse semigroup

Mathematics Subject Classification ID

Structure of general topological groups (22A05) Topological groups (topological aspects) (54H11) Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) (54A10) Extensions of spaces (compactifications, supercompactifications, completions, etc.) (54D35) Structure of topological semigroups (22A15) Inverse semigroups (20M18)

Related Items (3)

On feebly compact topologies on the semilattice \(\exp_{n_{\lambda}}\) ⋮ On countably compact 0-simple topological inverse semigroups ⋮ Pseudo-compactness, products and topological Brandt \(\lambda^0\)-extensions of semitopological monoids

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