On the Topology of a Compact Inverse Clifford Semigroup

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...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 1976-01, Vol.215, p.253-267
Main Author: Yeager, D. P.
Format: Article
Language:English
Subjects:
Algebra
Algebraic topology
Functors
Homomorphisms
Mathematical lattices
Morphisms
Semigroups
Topological compactness
Topological theorems
Topology
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Summary: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 → 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 → G to G: Y → G is a pair (ε, w) such that ε is a continuous homomorphism of X into Y and w is a natural transformation from F to Gε. 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.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-1976-0412331-0