On semitopological simple inverse ω-semigroups with compact maximal subgroups

2024/09/10 by Gutik, Oleg, Maksymyk, Kateryna
#20M18 #22A15 #54A10 #54D30 #54D40 #54D45 #54H11 #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2409.06344

Abstract

We describe the structure of (0-)simple inverse Hausdorff semitopological ω-semigroups with compact maximal subgroups. In particular, we show that if S is a simple inverse Hausdorff semitopological ω-semigroup with compact maximal subgroups, then S is topologically isomorphic to the Bruck--Reilly extension (BR(T,θ),τ_BR^⊕) of a finite semilattice T=[E;G_α,φ_α,β] of compact groups G_α in the class of topological inverse semigroups, where τ_BR^⊕ is the sum direct topology on BR(T,θ). Also we prove that every Hausdorff locally compact shift-continuous topology on the simple inverse Hausdorff semitopological ω-semigroups with compact maximal subgroups with adjoined zero is either compact or the zero is an isolated point.

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