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Normality on topological groups

dc.book.titleContribuciones matemáticas en honor a Juan Tarrés
dc.contributor.authorMartín Peinador, Elena
dc.date.accessioned2023-06-20T05:44:35Z
dc.date.available2023-06-20T05:44:35Z
dc.date.issued2012
dc.description.abstractIt is a well known fact that every topological group which satisfies a midl separation axiom like beint T0, is automatically Hausdorff and completely regular, thus, a Tychonoff space. Further separation axioms do not hold in general. For instance, the topological produt of uncountable many copies of the discrete group of integer numbers, say ZR is not normal. Clearly it is a topological Abelian Hausdorff group, with the operation defined pointwise and the product topology t. With this example in mind, one can ask, are there "many non-normal" groups? Markov asked in 1945 whether every uncountable abstract group admits a non-normal group topology. Van Douwen in 1990 asked if every Abelian group endowed with the weak topology corresponding to the family of all its homomorphisms in the unit circle of the complex plane should be normal. Here we prove that the above group ZR endowed with its Bohr topology tb is non-normal either, and obtain that all group topologies on ZR which lie between tb and the original one t are also non-normal. In fact, every compatible topology for this group lacks normality and we raise the general question about the "normality behaviour" of compatible group topologies.
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.facultyInstituto de Matemática Interdisciplinar (IMI)
dc.description.refereedTRUE
dc.description.sponsorshipMICINN of Spain
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/17384
dc.identifier.isbn978-84-695-4421-1
dc.identifier.relatedurlhttp://cisne.sim.ucm.es/record=b3232194~S6*spi
dc.identifier.urihttps://hdl.handle.net/20.500.14352/45370
dc.language.isoeng
dc.page.final293
dc.page.initial287
dc.page.total0
dc.publication.placeMadrid
dc.publisherUCM
dc.relation.projectIDMTM2009-14409-C01-02
dc.rights.accessRightsopen access
dc.subject.cdu514
dc.subject.cdu515.1
dc.subject.keywordPrecompact group
dc.subject.keywordNormal topological group
dc.subject.keywordBohr topology
dc.subject.keywordCompatible topology
dc.subject.keywordDuality
dc.subject.ucmGeometría
dc.subject.ucmTopología
dc.subject.unesco1204 Geometría
dc.subject.unesco1210 Topología
dc.titleNormality on topological groups
dc.typebook part
dspace.entity.typePublication
relation.isAuthorOfPublication0074400c-5caa-43fa-9c45-61c4b6f02093
relation.isAuthorOfPublication.latestForDiscovery0074400c-5caa-43fa-9c45-61c4b6f02093

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