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dc.contributor.authorFerreira, Maria João-
dc.contributor.authorGutiérrez García, Javier-
dc.contributor.authorPicado, Jorge-
dc.identifier.citationPré-Publicações DMUC. 08-42 (2008)en_US
dc.description.abstractUp to now point-free insertion results have been obtained only for semicontinuous real functions. Notably, there is now available a setting for dealing with arbitrary, not necessarily (semi-)continuous, point-free real functions, due to Guti errez Garc a, Kubiak and Picado, that gives point-free topology the freedom to deal with general real functions only available before to point-set topology. As a rst example of the usefulness of that setting, we apply it to characterize completely normal frames in terms of an insertion result for general real functions. This characterization extends a well known classical result of T. Kubiak about completely normal spaces. In addition, characterizations of completely normal frames that extend results of H. Simmons for topological spaces are presented. In particular, it follows that complete normality is a lattice-invariant property of spaces, correcting an erroneous conclusion in [Y.-M. Wong, Lattice-invariant properties of topological spaces, Proc. Amer. Math. Soc. 26 (1970) 206-208].en_US
dc.description.sponsorshipCentre of Mathematics of the University of Coimbra/FCT; Ministry of Education and Science of Spain; FEDER MTM2006-14925-C02-02; University of the Basque Country under grant GIU07/27en_US
dc.publisherCentro de Matemática da Universidade de Coimbraen_US
dc.subjectLocalic real functionen_US
dc.subjectNormal frameen_US
dc.subjectCompletely normal frameen_US
dc.subjectCompletely normal spaceen_US
dc.subjectExtremally disconnected frameen_US
dc.subjectUpper and lower regularizationsen_US
dc.titleCompletely normal frames and real-valued functionsen_US
item.fulltextCom Texto completo-
item.languageiso639-1en- de Ciências e Tecnologia, Universidade de Coimbra- de Coimbra- for Mathematics, University of Coimbra-
Appears in Collections:FCTUC Matemática - Vários
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