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Self-duality in the class of precompact groups
dc.contributor.author | Tkachenko, Mikhail | |
dc.date.accessioned | 2012-08-07T09:55:58Z | |
dc.date.available | 2012-08-07T09:55:58Z | |
dc.date.issued | 2009 | |
dc.identifier | http://dx.doi.org/10.1016/j.topol.2009.03.039 | |
dc.identifier.citation | Topology and its Applications, 156, 12, p. 2158-2165 | |
dc.identifier.issn | 1668641 | |
dc.identifier.uri | http://hdl.handle.net/10234/43728 | |
dc.description.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). 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. | |
dc.language.iso | eng | |
dc.publisher | Elsevier | |
dc.rights.uri | http://rightsstatements.org/vocab/CNE/1.0/ | * |
dc.subject | Countably compact | |
dc.subject | Countably pseudocompact | |
dc.subject | Dual group | |
dc.subject | MAP group | |
dc.subject | Precompact | |
dc.subject | Pseudocompact | |
dc.subject | Reflexive | |
dc.subject | Self-dual | |
dc.title | Self-duality in the class of precompact groups | |
dc.type | info:eu-repo/semantics/article | |
dc.identifier.doi | http://dx.doi.org/10.1016/j.topol.2009.03.039 | |
dc.rights.accessRights | info:eu-repo/semantics/restrictedAccess | |
dc.type.version | info:eu-repo/semantics/publishedVersion |
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