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C0-coarse geometry of complements of Z-sets in the Hilbert cube

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dc.contributor.authorCuchillo Ibáñez, Eduardo
dc.contributor.authorDydak, J.
dc.contributor.authorKoyama, A.
dc.contributor.authorAlonso Morón, Manuel
dc.date.accessioned2023-06-20T09:33:51Z
dc.date.available2023-06-20T09:33:51Z
dc.date.issued2008-10-10
dc.description.abstractMotivated by the Chapman Complement Theorem, we construct an isomorphism between the topological category of compact Z-sets in the Hilbert cube Q and the C0-coarse category of their complements. The C0-coarse morphisms are, in this particular case, intrinsically related to uniformly continuous proper maps. Using that fact we are able to relate in a natural way some of the topological invariants of Z-sets to the geometry of their complements.en
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipMEC
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/15176
dc.identifier.citationCuchillo Ibáñez, E., Dydak, J., Koyama, A. Alonso Morón, M. «$C_{0}$-Coarse Geometry of Complements of Z-Sets in the Hilbert Cube». Transactions of the American Mathematical Society, vol. 360, n.o 10, mayo de 2008, pp. 5229-46. DOI.org (Crossref), https://doi.org/10.1090/S0002-9947-08-04603-5.
dc.identifier.doi10.1090/S0002-9947-08-04603-5
dc.identifier.issn0002-9947
dc.identifier.officialurlhttps//doi.org/10.1090/S0002-9947-08-04603-5
dc.identifier.relatedurlhttp://www.ams.org/publications/journals/journalsframework/tran
dc.identifier.urihttps://hdl.handle.net/20.500.14352/49914
dc.issue.number10
dc.journal.titleTransactions of the American Mathematical Society
dc.language.isoeng
dc.page.final5246
dc.page.initial5229
dc.publisherAmerican Mathematical Society
dc.relation.projectIDMTM2006-0825
dc.rights.accessRightsrestricted access
dc.subject.cdu512.71
dc.subject.cdu515.171
dc.subject.keywordC0 coarse geometry
dc.subject.keywordCovering dimension
dc.subject.keywordAsymptotic dimension
dc.subject.keywordC0 coarse structure
dc.subject.keywordANR-space
dc.subject.keywordC0 coarse morphism
dc.subject.keywordUniformly continuous map
dc.subject.keywordCompact Z-set
dc.subject.keywordHigson-Roe compactification and corona
dc.subject.ucmTopología
dc.subject.unesco1210 Topología
dc.titleC0-coarse geometry of complements of Z-sets in the Hilbert cubeen
dc.typejournal article
dc.volume.number360
dspace.entity.typePublication
relation.isAuthorOfPublication95bd8189-3086-4e0f-94f6-06dee8c8f675
relation.isAuthorOfPublication.latestForDiscovery95bd8189-3086-4e0f-94f6-06dee8c8f675

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