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Pseudocompact group topologies with no infinite compact subsets
dc.contributor.author | Galindo, Jorge | |
dc.contributor.author | Macario, Sergio | |
dc.date.accessioned | 2011-07-29T09:38:27Z | |
dc.date.available | 2011-07-29T09:38:27Z | |
dc.date.issued | 2010-05 | |
dc.identifier.citation | arXiv:0812.5033v3 | |
dc.identifier.uri | http://hdl.handle.net/10234/26146 | |
dc.description.abstract | We show that every Abelian group satisfying a mild cardi- nal inequality admits a pseudocompact group topology from which all countable subgroups inherit the maximal totally bounded topology (we say that such a topology satisfies property ]). Every pseudocompact Abelian group G with cardinality |G| 22c satisfies this inequality and therefore admits a pseudocompact group topology with property ]. Under the Singular Cardinal Hypothesis (SCH) this criterion can be combined with an analysis of the algebraic structure of pseudocompact groups to prove that every pseudocompact Abelian group admits a pseudocompact group topology with property ]. We also observe that pseudocompact Abelian groups with property ] contain no infinite compact subsets and are examples of Pontryagin re- flexive precompact groups that are not compact. | |
dc.description.sponsorShip | Research supported by the Spanish Ministry of Science (including FEDER funds), grant MTM2008-04599/MTM and Fundaci´o Caixa Castell´o-Bancaixa, grant P1.1B2008-26. | |
dc.format.extent | 19 p. | |
dc.language.iso | eng | |
dc.rights.uri | http://rightsstatements.org/vocab/CNE/1.0/ | * |
dc.subject | G-dense | |
dc.subject | h-embedded | |
dc.subject | Compact Abelian group | |
dc.subject | #-property | |
dc.subject | SCH | |
dc.subject | Torsion-free rank | |
dc.subject | Dominant rank | |
dc.title | Pseudocompact group topologies with no infinite compact subsets | |
dc.type | info:eu-repo/semantics/article | |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
dc.type.version | info:eu-repo/semantics/sumittedVersion |
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