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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the topology of a compact inverse Clifford semigroup


Author: D. P. Yeager
Journal: Trans. Amer. Math. Soc. 215 (1976), 253-267
MSC: Primary 22A15
DOI: https://doi.org/10.1090/S0002-9947-1976-0412331-0
MathSciNet review: 0412331
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Abstract: A description of the topology of a compact inverse Clifford semigroup S is given in terms of the topologies of its subgroups and that of the semilattice X of idempotents. It is further shown that the category of compact inverse Clifford semigroups is equivalent to a full subcategory of the category whose objects are inverse limit preserving functors $ F:X \to G$, where X is a compact semilattice and G is the category of compact groups and continuous homomorphisms, and where a morphism from $ F:X \to G$ to $ G:Y \to G$ is a pair $ (\varepsilon ,w)$ such that $ \varepsilon $ is a continuous homomorphism of X into Y and w is a natural transformation from F to $ G\varepsilon $. Simpler descriptions of the topology of S are given in case the topology of X is first countable and in case the bonding maps between the maximal subgroups of S are open mappings.


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DOI: https://doi.org/10.1090/S0002-9947-1976-0412331-0
Keywords: Compact semilattice, compact inverse Clifford semigroup, inverse-limit-preserving functor
Article copyright: © Copyright 1976 American Mathematical Society