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 , where *X* is a compact semilattice and *G* is the category of compact groups and continuous homomorphisms, and where a morphism from to is a pair such that is a continuous homomorphism of *X* into *Y* and *w* is a natural transformation from *F* to . 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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Additional Information

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