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Title: Completely normal frames and real-valued functions
Authors: Ferreira, Maria João 
Gutiérrez García, Javier 
Picado, Jorge 
Keywords: Frame; Localic real function; Normal frame; Completely normal frame; Completely normal space; Extremally disconnected frame; Insertion; Upper and lower regularizations
Issue Date: 2008
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 08-42 (2008)
Abstract: Up 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].
Rights: openAccess
Appears in Collections:FCTUC Matemática - Vários

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