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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 | 2012-09-19T11:14:40Z | |
dc.date.available | 2012-09-19T11:14:40Z | |
dc.date.issued | 2011 | |
dc.identifier.citation | Journal of Pure and Applied Algebra (Apr. 2011) vol. 215, no. 4, p. 655-663 | ca_CA |
dc.identifier.issn | 0022-4049 | |
dc.identifier.other | arXiv:0812.5033v3 | |
dc.identifier.uri | http://hdl.handle.net/10234/47563 | |
dc.description.abstract | We show that every Abelian group satisfying a mild cardinal 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 reflexive precompact groups that are not compact. | ca_CA |
dc.format.extent | 19 p. | ca_CA |
dc.format.mimetype | application/pdf | ca_CA |
dc.language.iso | eng | ca_CA |
dc.publisher | Elsevier | ca_CA |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | * |
dc.subject | Abelian group | ca_CA |
dc.subject | Pseudocompact group | ca_CA |
dc.subject | Topology | ca_CA |
dc.title | Pseudocompact group topologies with no infinite compact subsets | ca_CA |
dc.type | info:eu-repo/semantics/article | ca_CA |
dc.identifier.doi | http://dx.doi.org/10.1016/j.jpaa.2010.06.014 | |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca_CA |
dc.relation.publisherVersion | http://www.sciencedirect.com/science/article/pii/S0022404910001271 | ca_CA |
dc.type.version | info:eu-repo/semantics/submittedVersion |
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