On semitopological simple inverse ω-semigroups with compact maximal subgroups
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 a simple inverse Hausdorff semitopological ω-semigroup with compact maximal subgroups with adjoined zero is either compact or the zero is an isolated point. , number=1, journal=Carpathian Mathematical Publications, author=Gutik, O.V. and Maksymyk, K.M., year=2025, month=Jun., pages=110–127