Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/43797
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dc.contributor.authorGutiérrez García, Javier-
dc.contributor.authorMozo Carollo, Imanol-
dc.contributor.authorPicado, Jorge-
dc.date.accessioned2017-10-09T15:16:29Z-
dc.date.issued2016-
dc.identifier10.1007/s00012-016-0378-z-
dc.identifier.urihttp://hdl.handle.net/10316/43797-
dc.description.abstractThis paper supplements an earlier one by the authors which constructed the Dedekind completion of the ring of continuous real functions on an arbitrary frame L in terms of partial continuous real functions on L. In the present paper, we provide three alternative views of it, in terms of (i) normal semicontinuous real functions on L, (ii) the Booleanization of L (in the case of bounded real functions) and the Gleason cover of L (in the general case), and (iii) Hausdorff continuous partial real functions on L. The first is the normal completion and extends Dilworth’s classical construction to the pointfree setting. The second shows that in the bounded case, the Dedekind completion is isomorphic to the lattice of bounded continuous real functions on the Booleanization of L, and that in the non-bounded case, it is isomorphic to the lattice of continuous real functions on the Gleason cover of L. Finally, the third is the pointfree version of Anguelov’s approach in terms of interval-valued functions. Two new classes of frames, cb-frames and weak cb-frames, emerge naturally in the first two representations. We show that they are conservative generalizations of their classical counterparts.por
dc.language.isoengpor
dc.publisherSpringerpor
dc.relationinfo:eu-repo/grantAgreement/FCT/COMPETE/132981/PTpor
dc.rightsembargoedAccess-
dc.titleNormal semicontinuity and the Dedekind completion of pointfree function ringspor
dc.typearticle-
degois.publication.firstPage301por
degois.publication.lastPage330por
degois.publication.issue3por
degois.publication.titleAlgebra universalispor
dc.relation.publisherversionhttps://link.springer.com/article/10.1007/s00012-016-0378-zpor
dc.peerreviewedyespor
dc.identifier.doi10.1007/s00012-016-0378-zpor
degois.publication.volume75por
dc.date.embargo2018-10-09T15:16:29Z-
item.languageiso639-1en-
item.fulltextCom Texto completo-
item.grantfulltextopen-
crisitem.author.deptFaculdade de Ciências e Tecnologia, Universidade de Coimbra-
crisitem.author.parentdeptUniversidade de Coimbra-
crisitem.author.researchunitCenter for Mathematics, University of Coimbra-
crisitem.author.orcid0000-0001-7837-1221-
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais
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