Character semigroups of locally compact inverse semigroups
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- by Ronald O. Fulp
- Proc. Amer. Math. Soc. 27 (1971), 613-618
- DOI: https://doi.org/10.1090/S0002-9939-1971-0276401-3
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Abstract:
We show that if $S$ is a locally compact abelian continuous-inverse semigroup whose idempotent semigroup $E$ satisfies a certain technical condition on its prime ideals, then the maximal subgroups of the character semigroup $S^\wedge$ of $S$ are obtained as inverse limits of the duals of the maximal subgroups of $S$. It is shown that the technical conditions on $E$ are satisfied in each of the following cases: $E$ is compact, $E$ is totally disconnected, or $E$ is a chain. We then obtain necessary and sufficient conditions in order that a given inverse system of compact groups indexed by a totally disconnected semilattice $E$ admit a compatible compact semigroup topology on their disjoint union.References
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Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 27 (1971), 613-618
- MSC: Primary 22.05
- DOI: https://doi.org/10.1090/S0002-9939-1971-0276401-3
- MathSciNet review: 0276401