Self-duality in the class of precompact groups
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http://dx.doi.org/10.1016/j.topol.2009.03.039 |
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Title
Self-duality in the class of precompact groupsAuthor (s)
Date
2009Publisher
ElsevierISSN
1668641Bibliographic citation
Topology and its Applications, 156, 12, p. 2158-2165Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/publishedVersionSubject
Abstract
A topological Abelian group G is called (strongly) self-dual if there exists a topological isomorphism Φ : G → G<sup>∧</sup> of G onto the dual group G<sup>∧</sup> (such that Φ (x) (y) = Φ (y) (x) for all x, y ∈ G). ... [+]
A topological Abelian group G is called (strongly) self-dual if there exists a topological isomorphism Φ : G → G<sup>∧</sup> of G onto the dual group G<sup>∧</sup> (such that Φ (x) (y) = Φ (y) (x) for all x, y ∈ G). We prove that every countably compact self-dual Abelian group is finite. It turns out, however, that for every infinite cardinal κ with κ<sup>ω</sup> = κ, there exists a pseudocompact, non-compact, strongly self-dual Boolean group of cardinality κ. © 2009 Elsevier B.V. All rights reserved. [-]
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